En el primer código, tomaré una población con 20 conglomerados y estudiaré estimaciones del total verdadero comparando si la media es única bajo parámetros de media similar. Al realizar el muestreo se toman 600 unidades elementales y los totales estimados son similares al total verdadero y sus varianzas bietápicas poco difieren.
N1=500
a1=sample(1:50,1)/50
b=a1/100
x1=rgamma(N1,a1,b)
N2=1500
a2=sample(1:50,1)/50
b=a2/100
x2=rgamma(N2,a2,b)
N3=2500
a3=sample(1:50,1)/50
b=a3/100
x3=rgamma(N3,a3,b)
N4=3500
a4=sample(1:50,1)/50
b=a4/100
x4=rgamma(N4,a4,b)
N5=5500
a5=sample(1:50,1)/50
b=a5/100
x5=rgamma(N5,a5,b)
N6=4500
a6=sample(1:50,1)/50
b=a6/100
x6=rgamma(N6,a6,b)
N7=6500
a7=sample(1:50,1)/50
b=a7/100
x7=rgamma(N7,a7,b)
N8=7500
a8=sample(1:50,1)/50
b=a8/100
x8=rgamma(N8,a8,b)
N9=8500
a9=sample(1:50,1)/50
b=a9/100
x9=rgamma(N9,a9,b)
N10=9500
a10=sample(1:50,1)/50
b=a10/100
x10=rgamma(N10,a10,b)
N11=10500
a11=sample(1:50,1)/50
b=a11/100
x11=rgamma(N11,a11,b)
N12=11500
a12=sample(1:50,1)/50
b=a12/100
x12=rgamma(N12,a12,b)
N13=12500
a13=sample(1:50,1)/50
b=a13/100
x13=rgamma(N13,a13,b)
N14=13500
a14=sample(1:50,1)/50
b=a14/100
x14=rgamma(N14,a14,b)
N15=14500
a15=sample(1:50,1)/50
b=a15/100
x15=rgamma(N15,a15,b)
N16=15500
a16=sample(1:50,1)/50
b=a16/100
x16=rgamma(N16,a16,b)
N17=16500
a17=sample(1:50,1)/50
b=a17/100
x17=rgamma(N17,a17,b)
N18=17500
a18=sample(1:50,1)/50
b=a18/100
x18=rgamma(N18,a18,b)
N19=18500
a19=sample(1:50,1)/50
b=a19/100
x19=rgamma(N19,a19,b)
N20=19500
a20=sample(1:50,1)/50
b=a20/100
x20=rgamma(N20,a20,b)
cc=c(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,x20)
T=sum(cc)
M=N1+N2+N3+N4+N5+N6+N7+N8+N9+N10+N11+N12+N13+N14+N15+N16+N17+N18+N19+N20
y1=sample(x1, 200, replace = FALSE)
y2=sample(x2, 200, replace = FALSE)
y3=sample(x3, 200, replace = FALSE)
c1=c(y1,y2,y3)
y1=sample(x1, 150, replace = FALSE)
y2=sample(x2, 150, replace = FALSE)
y3=sample(x3, 150, replace = FALSE)
y4=sample(x4, 150, replace = FALSE)
c2=c(y1,y2,y3,y4)
y1=sample(x1, 120, replace = FALSE)
y2=sample(x2, 120, replace = FALSE)
y3=sample(x3, 120, replace = FALSE)
y4=sample(x4, 120, replace = FALSE)
y5=sample(x5, 120, replace = FALSE)
c3=c(y1,y2,y3,y4,y5)
y1=sample(x1, 100, replace = FALSE)
y2=sample(x2, 100, replace = FALSE)
y3=sample(x3, 100, replace = FALSE)
y4=sample(x4, 100, replace = FALSE)
y5=sample(x5, 100, replace = FALSE)
y6=sample(x6, 100, replace = FALSE)
c4=c(y1,y2,y3,y4,y5,y6)
y1=sample(x1, 60, replace = FALSE)
y2=sample(x2, 60, replace = FALSE)
y3=sample(x3, 60, replace = FALSE)
y4=sample(x4, 60, replace = FALSE)
y5=sample(x5, 60, replace = FALSE)
y6=sample(x6, 60, replace = FALSE)
y7=sample(x7, 60, replace = FALSE)
y8=sample(x8, 60, replace = FALSE)
y9=sample(x9, 60, replace = FALSE)
y10=sample(x10, 60, replace = FALSE)
c5=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10)
y1=sample(x1, 50, replace = FALSE)
y2=sample(x2, 50, replace = FALSE)
y3=sample(x3, 50, replace = FALSE)
y4=sample(x4, 50, replace = FALSE)
y5=sample(x5, 50, replace = FALSE)
y6=sample(x6, 50, replace = FALSE)
y7=sample(x7, 50, replace = FALSE)
y8=sample(x8, 50, replace = FALSE)
y9=sample(x9, 50, replace = FALSE)
y10=sample(x10, 50, replace = FALSE)
y11=sample(x11, 50, replace = FALSE)
y12=sample(x12, 50, replace = FALSE)
c6=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12)
y1=sample(x1, 40, replace = FALSE)
y2=sample(x2, 40, replace = FALSE)
y3=sample(x3, 40, replace = FALSE)
y4=sample(x4, 40, replace = FALSE)
y5=sample(x5, 40, replace = FALSE)
y6=sample(x6, 40, replace = FALSE)
y7=sample(x7, 40, replace = FALSE)
y8=sample(x8, 40, replace = FALSE)
y9=sample(x9, 40, replace = FALSE)
y10=sample(x10, 40, replace = FALSE)
y11=sample(x11, 40, replace = FALSE)
y12=sample(x12, 40, replace = FALSE)
y13=sample(x13, 40, replace = FALSE)
y14=sample(x14, 40, replace = FALSE)
y15=sample(x15, 40, replace = FALSE)
c7=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15)
y1=sample(x1, 30, replace = FALSE)
y2=sample(x2, 30, replace = FALSE)
y3=sample(x3, 30, replace = FALSE)
y4=sample(x4, 30, replace = FALSE)
y5=sample(x5, 30, replace = FALSE)
y6=sample(x6, 30, replace = FALSE)
y7=sample(x7, 30, replace = FALSE)
y8=sample(x8, 30, replace = FALSE)
y9=sample(x9, 30, replace = FALSE)
y10=sample(x10, 30, replace = FALSE)
y11=sample(x11, 30, replace = FALSE)
y12=sample(x12, 30, replace = FALSE)
y13=sample(x13, 30, replace = FALSE)
y14=sample(x14, 30, replace = FALSE)
y15=sample(x15, 30, replace = FALSE)
y16=sample(x16, 30, replace = FALSE)
y17=sample(x17, 30, replace = FALSE)
y18=sample(x18, 30, replace = FALSE)
y19=sample(x19, 30, replace = FALSE)
y20=sample(x20, 30, replace = FALSE)
c8=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16,y17,y18,y19,y20)
t1=M*mean(c1); v1=M^2*(1-3/20)*var(c(mean(y1),mean(y2),mean(y3)))/3+M^2/3^2*sum(c(var(y1),var(y2),var(y3)))/200; v1x=M^2/3^2*sum(c(var(y1),var(y2),var(y3)))/200
t2=M*mean(c2); v2=M^2*(1-4/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4)))/4+M^2/4^2*sum(c(var(y1),var(y2),var(y3),var(y4)))/150;v2x=M^2/4^2*sum(c(var(y1),var(y2),var(y3),var(y4)))/150
t3=M*mean(c3); v3=M^2*(1-5/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5)))/5+M^2/5^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5)))/120;v3x=M^2/5^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5)))/120
t4=M*mean(c4); v4=M^2*(1-6/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6)))/6+M^2/6^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6)))/100; v4x=M^2/6^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6)))/100
t5=M*mean(c5); v5=M^2*(1-10/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10)))/10+M^2/10^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10)))/60;v5x=M^2/10^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10)))/60
t6=M*mean(c6); v6=M^2*(1-12/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12)))/12+M^2/12^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12)))/50;v6x=M^2/12^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12)))/50
t7=M*mean(c7); v7=M^2*(1-15/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12),mean(y13),mean(y14),mean(y15)))/15+M^2/15^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15)))/40;v7x=M^2/15^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15)))/40
t8=M*mean(c8); v8=M^2*(1-20/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12),mean(y13),mean(y14),mean(y15)))/15+M^2/20^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15),var(y16),var(y17),var(y18),var(y19),var(y20)))/30
cx1=cbind(rbind(n1=3, m1=200,t1,v1,v1x),rbind(n2=4,m2=150,t2,v2,v2x),rbind(n3=5,m3=120,t3,v3,v3x),rbind(n4=6,m4=100,t4,v4,v4x),rbind(n5=10,m6=60,t5,v5,v5x),rbind(n6=12,m6=50,t6,v6,v6x),rbind(n7=15,m7=40,t7,v7,v7x),rbind(n8=20,m8=30,t8,v8,v8))
y1=sample(x1, 200, replace = FALSE)
y2=sample(x2, 200, replace = FALSE)
y3=sample(x3, 200, replace = FALSE)
c1=c(y1,y2,y3)
y1=sample(x1, 150, replace = FALSE)
y2=sample(x2, 150, replace = FALSE)
y3=sample(x3, 150, replace = FALSE)
y4=sample(x4, 150, replace = FALSE)
c2=c(y1,y2,y3,y4)
y1=sample(x1, 120, replace = FALSE)
y2=sample(x2, 120, replace = FALSE)
y3=sample(x3, 120, replace = FALSE)
y4=sample(x4, 120, replace = FALSE)
y5=sample(x5, 120, replace = FALSE)
c3=c(y1,y2,y3,y4,y5)
y1=sample(x1, 100, replace = FALSE)
y2=sample(x2, 100, replace = FALSE)
y3=sample(x3, 100, replace = FALSE)
y4=sample(x4, 100, replace = FALSE)
y5=sample(x5, 100, replace = FALSE)
y6=sample(x6, 100, replace = FALSE)
c4=c(y1,y2,y3,y4,y5,y6)
y1=sample(x1, 60, replace = FALSE)
y2=sample(x2, 60, replace = FALSE)
y3=sample(x3, 60, replace = FALSE)
y4=sample(x4, 60, replace = FALSE)
y5=sample(x5, 60, replace = FALSE)
y6=sample(x6, 60, replace = FALSE)
y7=sample(x7, 60, replace = FALSE)
y8=sample(x8, 60, replace = FALSE)
y9=sample(x9, 60, replace = FALSE)
y10=sample(x10, 60, replace = FALSE)
c5=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10)
y1=sample(x1, 50, replace = FALSE)
y2=sample(x2, 50, replace = FALSE)
y3=sample(x3, 50, replace = FALSE)
y4=sample(x4, 50, replace = FALSE)
y5=sample(x5, 50, replace = FALSE)
y6=sample(x6, 50, replace = FALSE)
y7=sample(x7, 50, replace = FALSE)
y8=sample(x8, 50, replace = FALSE)
y9=sample(x9, 50, replace = FALSE)
y10=sample(x10, 50, replace = FALSE)
y11=sample(x11, 50, replace = FALSE)
y12=sample(x12, 50, replace = FALSE)
c6=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12)
y1=sample(x1, 40, replace = FALSE)
y2=sample(x2, 40, replace = FALSE)
y3=sample(x3, 40, replace = FALSE)
y4=sample(x4, 40, replace = FALSE)
y5=sample(x5, 40, replace = FALSE)
y6=sample(x6, 40, replace = FALSE)
y7=sample(x7, 40, replace = FALSE)
y8=sample(x8, 40, replace = FALSE)
y9=sample(x9, 40, replace = FALSE)
y10=sample(x10, 40, replace = FALSE)
y11=sample(x11, 40, replace = FALSE)
y12=sample(x12, 40, replace = FALSE)
y13=sample(x13, 40, replace = FALSE)
y14=sample(x14, 40, replace = FALSE)
y15=sample(x15, 40, replace = FALSE)
c7=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15)
y1=sample(x1, 30, replace = FALSE)
y2=sample(x2, 30, replace = FALSE)
y3=sample(x3, 30, replace = FALSE)
y4=sample(x4, 30, replace = FALSE)
y5=sample(x5, 30, replace = FALSE)
y6=sample(x6, 30, replace = FALSE)
y7=sample(x7, 30, replace = FALSE)
y8=sample(x8, 30, replace = FALSE)
y9=sample(x9, 30, replace = FALSE)
y10=sample(x10, 30, replace = FALSE)
y11=sample(x11, 30, replace = FALSE)
y12=sample(x12, 30, replace = FALSE)
y13=sample(x13, 30, replace = FALSE)
y14=sample(x14, 30, replace = FALSE)
y15=sample(x15, 30, replace = FALSE)
y16=sample(x16, 30, replace = FALSE)
y17=sample(x17, 30, replace = FALSE)
y18=sample(x18, 30, replace = FALSE)
y19=sample(x19, 30, replace = FALSE)
y20=sample(x20, 30, replace = FALSE)
c8=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16,y17,y18,y19,y20)
t1=M*mean(c1); v1=M^2*(1-3/20)*var(c(mean(y1),mean(y2),mean(y3)))/3+M^2/3^2*sum(c(var(y1),var(y2),var(y3)))/200; v1x=M^2/3^2*sum(c(var(y1),var(y2),var(y3)))/200
t2=M*mean(c2); v2=M^2*(1-4/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4)))/4+M^2/4^2*sum(c(var(y1),var(y2),var(y3),var(y4)))/150;v2x=M^2/4^2*sum(c(var(y1),var(y2),var(y3),var(y4)))/150
t3=M*mean(c3); v3=M^2*(1-5/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5)))/5+M^2/5^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5)))/120;v3x=M^2/5^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5)))/120
t4=M*mean(c4); v4=M^2*(1-6/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6)))/6+M^2/6^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6)))/100; v4x=M^2/6^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6)))/100
t5=M*mean(c5); v5=M^2*(1-10/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10)))/10+M^2/10^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10)))/60;v5x=M^2/10^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10)))/60
t6=M*mean(c6); v6=M^2*(1-12/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12)))/12+M^2/12^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12)))/50;v6x=M^2/12^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12)))/50
t7=M*mean(c7); v7=M^2*(1-15/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12),mean(y13),mean(y14),mean(y15)))/15+M^2/15^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15)))/40;v7x=M^2/15^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15)))/40
t8=M*mean(c8); v8=M^2*(1-20/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12),mean(y13),mean(y14),mean(y15)))/15+M^2/20^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15),var(y16),var(y17),var(y18),var(y19),var(y20)))/30
cx2=cbind(rbind(n1=3, m1=200,t1,v1,v1x),rbind(n2=4,m2=150,t2,v2,v2x),rbind(n3=5,m3=120,t3,v3,v3x),rbind(n4=6,m4=100,t4,v4,v4x),rbind(n5=10,m6=60,t5,v5,v5x),rbind(n6=12,m6=50,t6,v6,v6x),rbind(n7=15,m7=40,t7,v7,v7x),rbind(n8=20,m8=30,t8,v8,v8))
y1=sample(x1, 200, replace = FALSE)
y2=sample(x2, 200, replace = FALSE)
y3=sample(x3, 200, replace = FALSE)
c1=c(y1,y2,y3)
y1=sample(x1, 150, replace = FALSE)
y2=sample(x2, 150, replace = FALSE)
y3=sample(x3, 150, replace = FALSE)
y4=sample(x4, 150, replace = FALSE)
c2=c(y1,y2,y3,y4)
y1=sample(x1, 120, replace = FALSE)
y2=sample(x2, 120, replace = FALSE)
y3=sample(x3, 120, replace = FALSE)
y4=sample(x4, 120, replace = FALSE)
y5=sample(x5, 120, replace = FALSE)
c3=c(y1,y2,y3,y4,y5)
y1=sample(x1, 100, replace = FALSE)
y2=sample(x2, 100, replace = FALSE)
y3=sample(x3, 100, replace = FALSE)
y4=sample(x4, 100, replace = FALSE)
y5=sample(x5, 100, replace = FALSE)
y6=sample(x6, 100, replace = FALSE)
c4=c(y1,y2,y3,y4,y5,y6)
y1=sample(x1, 60, replace = FALSE)
y2=sample(x2, 60, replace = FALSE)
y3=sample(x3, 60, replace = FALSE)
y4=sample(x4, 60, replace = FALSE)
y5=sample(x5, 60, replace = FALSE)
y6=sample(x6, 60, replace = FALSE)
y7=sample(x7, 60, replace = FALSE)
y8=sample(x8, 60, replace = FALSE)
y9=sample(x9, 60, replace = FALSE)
y10=sample(x10, 60, replace = FALSE)
c5=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10)
y1=sample(x1, 50, replace = FALSE)
y2=sample(x2, 50, replace = FALSE)
y3=sample(x3, 50, replace = FALSE)
y4=sample(x4, 50, replace = FALSE)
y5=sample(x5, 50, replace = FALSE)
y6=sample(x6, 50, replace = FALSE)
y7=sample(x7, 50, replace = FALSE)
y8=sample(x8, 50, replace = FALSE)
y9=sample(x9, 50, replace = FALSE)
y10=sample(x10, 50, replace = FALSE)
y11=sample(x11, 50, replace = FALSE)
y12=sample(x12, 50, replace = FALSE)
c6=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12)
y1=sample(x1, 40, replace = FALSE)
y2=sample(x2, 40, replace = FALSE)
y3=sample(x3, 40, replace = FALSE)
y4=sample(x4, 40, replace = FALSE)
y5=sample(x5, 40, replace = FALSE)
y6=sample(x6, 40, replace = FALSE)
y7=sample(x7, 40, replace = FALSE)
y8=sample(x8, 40, replace = FALSE)
y9=sample(x9, 40, replace = FALSE)
y10=sample(x10, 40, replace = FALSE)
y11=sample(x11, 40, replace = FALSE)
y12=sample(x12, 40, replace = FALSE)
y13=sample(x13, 40, replace = FALSE)
y14=sample(x14, 40, replace = FALSE)
y15=sample(x15, 40, replace = FALSE)
c7=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15)
y1=sample(x1, 30, replace = FALSE)
y2=sample(x2, 30, replace = FALSE)
y3=sample(x3, 30, replace = FALSE)
y4=sample(x4, 30, replace = FALSE)
y5=sample(x5, 30, replace = FALSE)
y6=sample(x6, 30, replace = FALSE)
y7=sample(x7, 30, replace = FALSE)
y8=sample(x8, 30, replace = FALSE)
y9=sample(x9, 30, replace = FALSE)
y10=sample(x10, 30, replace = FALSE)
y11=sample(x11, 30, replace = FALSE)
y12=sample(x12, 30, replace = FALSE)
y13=sample(x13, 30, replace = FALSE)
y14=sample(x14, 30, replace = FALSE)
y15=sample(x15, 30, replace = FALSE)
y16=sample(x16, 30, replace = FALSE)
y17=sample(x17, 30, replace = FALSE)
y18=sample(x18, 30, replace = FALSE)
y19=sample(x19, 30, replace = FALSE)
y20=sample(x20, 30, replace = FALSE)
c8=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16,y17,y18,y19,y20)
t1=M*mean(c1); v1=M^2*(1-3/20)*var(c(mean(y1),mean(y2),mean(y3)))/3+M^2/3^2*sum(c(var(y1),var(y2),var(y3)))/200; v1x=M^2/3^2*sum(c(var(y1),var(y2),var(y3)))/200
t2=M*mean(c2); v2=M^2*(1-4/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4)))/4+M^2/4^2*sum(c(var(y1),var(y2),var(y3),var(y4)))/150;v2x=M^2/4^2*sum(c(var(y1),var(y2),var(y3),var(y4)))/150
t3=M*mean(c3); v3=M^2*(1-5/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5)))/5+M^2/5^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5)))/120;v3x=M^2/5^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5)))/120
t4=M*mean(c4); v4=M^2*(1-6/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6)))/6+M^2/6^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6)))/100; v4x=M^2/6^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6)))/100
t5=M*mean(c5); v5=M^2*(1-10/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10)))/10+M^2/10^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10)))/60;v5x=M^2/10^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10)))/60
t6=M*mean(c6); v6=M^2*(1-12/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12)))/12+M^2/12^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12)))/50;v6x=M^2/12^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12)))/50
t7=M*mean(c7); v7=M^2*(1-15/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12),mean(y13),mean(y14),mean(y15)))/15+M^2/15^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15)))/40;v7x=M^2/15^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15)))/40
t8=M*mean(c8); v8=M^2*(1-20/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12),mean(y13),mean(y14),mean(y15)))/15+M^2/20^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15),var(y16),var(y17),var(y18),var(y19),var(y20)))/30
cx3=cbind(rbind(n1=3, m1=200,t1,v1,v1x),rbind(n2=4,m2=150,t2,v2,v2x),rbind(n3=5,m3=120,t3,v3,v3x),rbind(n4=6,m4=100,t4,v4,v4x),rbind(n5=10,m6=60,t5,v5,v5x),rbind(n6=12,m6=50,t6,v6,v6x),rbind(n7=15,m7=40,t7,v7,v7x),rbind(n8=20,m8=30,t8,v8,v8))
y1=sample(x1, 200, replace = FALSE)
y2=sample(x2, 200, replace = FALSE)
y3=sample(x3, 200, replace = FALSE)
c1=c(y1,y2,y3)
y1=sample(x1, 150, replace = FALSE)
y2=sample(x2, 150, replace = FALSE)
y3=sample(x3, 150, replace = FALSE)
y4=sample(x4, 150, replace = FALSE)
c2=c(y1,y2,y3,y4)
y1=sample(x1, 120, replace = FALSE)
y2=sample(x2, 120, replace = FALSE)
y3=sample(x3, 120, replace = FALSE)
y4=sample(x4, 120, replace = FALSE)
y5=sample(x5, 120, replace = FALSE)
c3=c(y1,y2,y3,y4,y5)
y1=sample(x1, 100, replace = FALSE)
y2=sample(x2, 100, replace = FALSE)
y3=sample(x3, 100, replace = FALSE)
y4=sample(x4, 100, replace = FALSE)
y5=sample(x5, 100, replace = FALSE)
y6=sample(x6, 100, replace = FALSE)
c4=c(y1,y2,y3,y4,y5,y6)
y1=sample(x1, 60, replace = FALSE)
y2=sample(x2, 60, replace = FALSE)
y3=sample(x3, 60, replace = FALSE)
y4=sample(x4, 60, replace = FALSE)
y5=sample(x5, 60, replace = FALSE)
y6=sample(x6, 60, replace = FALSE)
y7=sample(x7, 60, replace = FALSE)
y8=sample(x8, 60, replace = FALSE)
y9=sample(x9, 60, replace = FALSE)
y10=sample(x10, 60, replace = FALSE)
c5=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10)
y1=sample(x1, 50, replace = FALSE)
y2=sample(x2, 50, replace = FALSE)
y3=sample(x3, 50, replace = FALSE)
y4=sample(x4, 50, replace = FALSE)
y5=sample(x5, 50, replace = FALSE)
y6=sample(x6, 50, replace = FALSE)
y7=sample(x7, 50, replace = FALSE)
y8=sample(x8, 50, replace = FALSE)
y9=sample(x9, 50, replace = FALSE)
y10=sample(x10, 50, replace = FALSE)
y11=sample(x11, 50, replace = FALSE)
y12=sample(x12, 50, replace = FALSE)
c6=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12)
y1=sample(x1, 40, replace = FALSE)
y2=sample(x2, 40, replace = FALSE)
y3=sample(x3, 40, replace = FALSE)
y4=sample(x4, 40, replace = FALSE)
y5=sample(x5, 40, replace = FALSE)
y6=sample(x6, 40, replace = FALSE)
y7=sample(x7, 40, replace = FALSE)
y8=sample(x8, 40, replace = FALSE)
y9=sample(x9, 40, replace = FALSE)
y10=sample(x10, 40, replace = FALSE)
y11=sample(x11, 40, replace = FALSE)
y12=sample(x12, 40, replace = FALSE)
y13=sample(x13, 40, replace = FALSE)
y14=sample(x14, 40, replace = FALSE)
y15=sample(x15, 40, replace = FALSE)
c7=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15)
y1=sample(x1, 30, replace = FALSE)
y2=sample(x2, 30, replace = FALSE)
y3=sample(x3, 30, replace = FALSE)
y4=sample(x4, 30, replace = FALSE)
y5=sample(x5, 30, replace = FALSE)
y6=sample(x6, 30, replace = FALSE)
y7=sample(x7, 30, replace = FALSE)
y8=sample(x8, 30, replace = FALSE)
y9=sample(x9, 30, replace = FALSE)
y10=sample(x10, 30, replace = FALSE)
y11=sample(x11, 30, replace = FALSE)
y12=sample(x12, 30, replace = FALSE)
y13=sample(x13, 30, replace = FALSE)
y14=sample(x14, 30, replace = FALSE)
y15=sample(x15, 30, replace = FALSE)
y16=sample(x16, 30, replace = FALSE)
y17=sample(x17, 30, replace = FALSE)
y18=sample(x18, 30, replace = FALSE)
y19=sample(x19, 30, replace = FALSE)
y20=sample(x20, 30, replace = FALSE)
c8=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16,y17,y18,y19,y20)
t1=M*mean(c1); v1=M^2*(1-3/20)*var(c(mean(y1),mean(y2),mean(y3)))/3+M^2/3^2*sum(c(var(y1),var(y2),var(y3)))/200; v1x=M^2/3^2*sum(c(var(y1),var(y2),var(y3)))/200
t2=M*mean(c2); v2=M^2*(1-4/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4)))/4+M^2/4^2*sum(c(var(y1),var(y2),var(y3),var(y4)))/150;v2x=M^2/4^2*sum(c(var(y1),var(y2),var(y3),var(y4)))/150
t3=M*mean(c3); v3=M^2*(1-5/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5)))/5+M^2/5^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5)))/120;v3x=M^2/5^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5)))/120
t4=M*mean(c4); v4=M^2*(1-6/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6)))/6+M^2/6^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6)))/100; v4x=M^2/6^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6)))/100
t5=M*mean(c5); v5=M^2*(1-10/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10)))/10+M^2/10^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10)))/60;v5x=M^2/10^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10)))/60
t6=M*mean(c6); v6=M^2*(1-12/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12)))/12+M^2/12^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12)))/50;v6x=M^2/12^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12)))/50
t7=M*mean(c7); v7=M^2*(1-15/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12),mean(y13),mean(y14),mean(y15)))/15+M^2/15^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15)))/40;v7x=M^2/15^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15)))/40
t8=M*mean(c8); v8=M^2*(1-20/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12),mean(y13),mean(y14),mean(y15)))/15+M^2/20^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15),var(y16),var(y17),var(y18),var(y19),var(y20)))/30
cx4=cbind(rbind(n1=3, m1=200,t1,v1,v1x),rbind(n2=4,m2=150,t2,v2,v2x),rbind(n3=5,m3=120,t3,v3,v3x),rbind(n4=6,m4=100,t4,v4,v4x),rbind(n5=10,m6=60,t5,v5,v5x),rbind(n6=12,m6=50,t6,v6,v6x),rbind(n7=15,m7=40,t7,v7,v7x),rbind(n8=20,m8=30,t8,v8,v8))
y1=sample(x1, 200, replace = FALSE)
y2=sample(x2, 200, replace = FALSE)
y3=sample(x3, 200, replace = FALSE)
c1=c(y1,y2,y3)
y1=sample(x1, 150, replace = FALSE)
y2=sample(x2, 150, replace = FALSE)
y3=sample(x3, 150, replace = FALSE)
y4=sample(x4, 150, replace = FALSE)
c2=c(y1,y2,y3,y4)
y1=sample(x1, 120, replace = FALSE)
y2=sample(x2, 120, replace = FALSE)
y3=sample(x3, 120, replace = FALSE)
y4=sample(x4, 120, replace = FALSE)
y5=sample(x5, 120, replace = FALSE)
c3=c(y1,y2,y3,y4,y5)
y1=sample(x1, 100, replace = FALSE)
y2=sample(x2, 100, replace = FALSE)
y3=sample(x3, 100, replace = FALSE)
y4=sample(x4, 100, replace = FALSE)
y5=sample(x5, 100, replace = FALSE)
y6=sample(x6, 100, replace = FALSE)
c4=c(y1,y2,y3,y4,y5,y6)
y1=sample(x1, 60, replace = FALSE)
y2=sample(x2, 60, replace = FALSE)
y3=sample(x3, 60, replace = FALSE)
y4=sample(x4, 60, replace = FALSE)
y5=sample(x5, 60, replace = FALSE)
y6=sample(x6, 60, replace = FALSE)
y7=sample(x7, 60, replace = FALSE)
y8=sample(x8, 60, replace = FALSE)
y9=sample(x9, 60, replace = FALSE)
y10=sample(x10, 60, replace = FALSE)
c5=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10)
y1=sample(x1, 50, replace = FALSE)
y2=sample(x2, 50, replace = FALSE)
y3=sample(x3, 50, replace = FALSE)
y4=sample(x4, 50, replace = FALSE)
y5=sample(x5, 50, replace = FALSE)
y6=sample(x6, 50, replace = FALSE)
y7=sample(x7, 50, replace = FALSE)
y8=sample(x8, 50, replace = FALSE)
y9=sample(x9, 50, replace = FALSE)
y10=sample(x10, 50, replace = FALSE)
y11=sample(x11, 50, replace = FALSE)
y12=sample(x12, 50, replace = FALSE)
c6=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12)
y1=sample(x1, 40, replace = FALSE)
y2=sample(x2, 40, replace = FALSE)
y3=sample(x3, 40, replace = FALSE)
y4=sample(x4, 40, replace = FALSE)
y5=sample(x5, 40, replace = FALSE)
y6=sample(x6, 40, replace = FALSE)
y7=sample(x7, 40, replace = FALSE)
y8=sample(x8, 40, replace = FALSE)
y9=sample(x9, 40, replace = FALSE)
y10=sample(x10, 40, replace = FALSE)
y11=sample(x11, 40, replace = FALSE)
y12=sample(x12, 40, replace = FALSE)
y13=sample(x13, 40, replace = FALSE)
y14=sample(x14, 40, replace = FALSE)
y15=sample(x15, 40, replace = FALSE)
c7=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15)
y1=sample(x1, 30, replace = FALSE)
y2=sample(x2, 30, replace = FALSE)
y3=sample(x3, 30, replace = FALSE)
y4=sample(x4, 30, replace = FALSE)
y5=sample(x5, 30, replace = FALSE)
y6=sample(x6, 30, replace = FALSE)
y7=sample(x7, 30, replace = FALSE)
y8=sample(x8, 30, replace = FALSE)
y9=sample(x9, 30, replace = FALSE)
y10=sample(x10, 30, replace = FALSE)
y11=sample(x11, 30, replace = FALSE)
y12=sample(x12, 30, replace = FALSE)
y13=sample(x13, 30, replace = FALSE)
y14=sample(x14, 30, replace = FALSE)
y15=sample(x15, 30, replace = FALSE)
y16=sample(x16, 30, replace = FALSE)
y17=sample(x17, 30, replace = FALSE)
y18=sample(x18, 30, replace = FALSE)
y19=sample(x19, 30, replace = FALSE)
y20=sample(x20, 30, replace = FALSE)
c8=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16,y17,y18,y19,y20)
t1=M*mean(c1); v1=M^2*(1-3/20)*var(c(mean(y1),mean(y2),mean(y3)))/3+M^2/3^2*sum(c(var(y1),var(y2),var(y3)))/200; v1x=M^2/3^2*sum(c(var(y1),var(y2),var(y3)))/200
t2=M*mean(c2); v2=M^2*(1-4/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4)))/4+M^2/4^2*sum(c(var(y1),var(y2),var(y3),var(y4)))/150;v2x=M^2/4^2*sum(c(var(y1),var(y2),var(y3),var(y4)))/150
t3=M*mean(c3); v3=M^2*(1-5/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5)))/5+M^2/5^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5)))/120;v3x=M^2/5^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5)))/120
t4=M*mean(c4); v4=M^2*(1-6/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6)))/6+M^2/6^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6)))/100; v4x=M^2/6^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6)))/100
t5=M*mean(c5); v5=M^2*(1-10/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10)))/10+M^2/10^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10)))/60;v5x=M^2/10^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10)))/60
t6=M*mean(c6); v6=M^2*(1-12/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12)))/12+M^2/12^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12)))/50;v6x=M^2/12^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12)))/50
t7=M*mean(c7); v7=M^2*(1-15/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12),mean(y13),mean(y14),mean(y15)))/15+M^2/15^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15)))/40;v7x=M^2/15^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15)))/40
t8=M*mean(c8); v8=M^2*(1-20/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12),mean(y13),mean(y14),mean(y15)))/15+M^2/20^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15),var(y16),var(y17),var(y18),var(y19),var(y20)))/30
cx5=cbind(rbind(n1=3, m1=200,t1,v1,v1x),rbind(n2=4,m2=150,t2,v2,v2x),rbind(n3=5,m3=120,t3,v3,v3x),rbind(n4=6,m4=100,t4,v4,v4x),rbind(n5=10,m6=60,t5,v5,v5x),rbind(n6=12,m6=50,t6,v6,v6x),rbind(n7=15,m7=40,t7,v7,v7x),rbind(n8=20,m8=30,t8,v8,v8))
y1=sample(x1, 200, replace = FALSE)
y2=sample(x2, 200, replace = FALSE)
y3=sample(x3, 200, replace = FALSE)
c1=c(y1,y2,y3)
y1=sample(x1, 150, replace = FALSE)
y2=sample(x2, 150, replace = FALSE)
y3=sample(x3, 150, replace = FALSE)
y4=sample(x4, 150, replace = FALSE)
c2=c(y1,y2,y3,y4)
y1=sample(x1, 120, replace = FALSE)
y2=sample(x2, 120, replace = FALSE)
y3=sample(x3, 120, replace = FALSE)
y4=sample(x4, 120, replace = FALSE)
y5=sample(x5, 120, replace = FALSE)
c3=c(y1,y2,y3,y4,y5)
y1=sample(x1, 100, replace = FALSE)
y2=sample(x2, 100, replace = FALSE)
y3=sample(x3, 100, replace = FALSE)
y4=sample(x4, 100, replace = FALSE)
y5=sample(x5, 100, replace = FALSE)
y6=sample(x6, 100, replace = FALSE)
c4=c(y1,y2,y3,y4,y5,y6)
y1=sample(x1, 60, replace = FALSE)
y2=sample(x2, 60, replace = FALSE)
y3=sample(x3, 60, replace = FALSE)
y4=sample(x4, 60, replace = FALSE)
y5=sample(x5, 60, replace = FALSE)
y6=sample(x6, 60, replace = FALSE)
y7=sample(x7, 60, replace = FALSE)
y8=sample(x8, 60, replace = FALSE)
y9=sample(x9, 60, replace = FALSE)
y10=sample(x10, 60, replace = FALSE)
c5=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10)
y1=sample(x1, 50, replace = FALSE)
y2=sample(x2, 50, replace = FALSE)
y3=sample(x3, 50, replace = FALSE)
y4=sample(x4, 50, replace = FALSE)
y5=sample(x5, 50, replace = FALSE)
y6=sample(x6, 50, replace = FALSE)
y7=sample(x7, 50, replace = FALSE)
y8=sample(x8, 50, replace = FALSE)
y9=sample(x9, 50, replace = FALSE)
y10=sample(x10, 50, replace = FALSE)
y11=sample(x11, 50, replace = FALSE)
y12=sample(x12, 50, replace = FALSE)
c6=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12)
y1=sample(x1, 40, replace = FALSE)
y2=sample(x2, 40, replace = FALSE)
y3=sample(x3, 40, replace = FALSE)
y4=sample(x4, 40, replace = FALSE)
y5=sample(x5, 40, replace = FALSE)
y6=sample(x6, 40, replace = FALSE)
y7=sample(x7, 40, replace = FALSE)
y8=sample(x8, 40, replace = FALSE)
y9=sample(x9, 40, replace = FALSE)
y10=sample(x10, 40, replace = FALSE)
y11=sample(x11, 40, replace = FALSE)
y12=sample(x12, 40, replace = FALSE)
y13=sample(x13, 40, replace = FALSE)
y14=sample(x14, 40, replace = FALSE)
y15=sample(x15, 40, replace = FALSE)
c7=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15)
y1=sample(x1, 30, replace = FALSE)
y2=sample(x2, 30, replace = FALSE)
y3=sample(x3, 30, replace = FALSE)
y4=sample(x4, 30, replace = FALSE)
y5=sample(x5, 30, replace = FALSE)
y6=sample(x6, 30, replace = FALSE)
y7=sample(x7, 30, replace = FALSE)
y8=sample(x8, 30, replace = FALSE)
y9=sample(x9, 30, replace = FALSE)
y10=sample(x10, 30, replace = FALSE)
y11=sample(x11, 30, replace = FALSE)
y12=sample(x12, 30, replace = FALSE)
y13=sample(x13, 30, replace = FALSE)
y14=sample(x14, 30, replace = FALSE)
y15=sample(x15, 30, replace = FALSE)
y16=sample(x16, 30, replace = FALSE)
y17=sample(x17, 30, replace = FALSE)
y18=sample(x18, 30, replace = FALSE)
y19=sample(x19, 30, replace = FALSE)
y20=sample(x20, 30, replace = FALSE)
c8=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16,y17,y18,y19,y20)
t1=M*mean(c1); v1=M^2*(1-3/20)*var(c(mean(y1),mean(y2),mean(y3)))/3+M^2/3^2*sum(c(var(y1),var(y2),var(y3)))/200; v1x=M^2/3^2*sum(c(var(y1),var(y2),var(y3)))/200
t2=M*mean(c2); v2=M^2*(1-4/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4)))/4+M^2/4^2*sum(c(var(y1),var(y2),var(y3),var(y4)))/150;v2x=M^2/4^2*sum(c(var(y1),var(y2),var(y3),var(y4)))/150
t3=M*mean(c3); v3=M^2*(1-5/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5)))/5+M^2/5^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5)))/120;v3x=M^2/5^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5)))/120
t4=M*mean(c4); v4=M^2*(1-6/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6)))/6+M^2/6^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6)))/100; v4x=M^2/6^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6)))/100
t5=M*mean(c5); v5=M^2*(1-10/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10)))/10+M^2/10^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10)))/60;v5x=M^2/10^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10)))/60
t6=M*mean(c6); v6=M^2*(1-12/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12)))/12+M^2/12^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12)))/50;v6x=M^2/12^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12)))/50
t7=M*mean(c7); v7=M^2*(1-15/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12),mean(y13),mean(y14),mean(y15)))/15+M^2/15^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15)))/40;v7x=M^2/15^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15)))/40
t8=M*mean(c8); v8=M^2*(1-20/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12),mean(y13),mean(y14),mean(y15)))/15+M^2/20^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15),var(y16),var(y17),var(y18),var(y19),var(y20)))/30
cx6=cbind(rbind(n1=3, m1=200,t1,v1,v1x),rbind(n2=4,m2=150,t2,v2,v2x),rbind(n3=5,m3=120,t3,v3,v3x),rbind(n4=6,m4=100,t4,v4,v4x),rbind(n5=10,m6=60,t5,v5,v5x),rbind(n6=12,m6=50,t6,v6,v6x),rbind(n7=15,m7=40,t7,v7,v7x),rbind(n8=20,m8=30,t8,v8,v8))
y1=sample(x1, 200, replace = FALSE)
y2=sample(x2, 200, replace = FALSE)
y3=sample(x3, 200, replace = FALSE)
c1=c(y1,y2,y3)
y1=sample(x1, 150, replace = FALSE)
y2=sample(x2, 150, replace = FALSE)
y3=sample(x3, 150, replace = FALSE)
y4=sample(x4, 150, replace = FALSE)
c2=c(y1,y2,y3,y4)
y1=sample(x1, 120, replace = FALSE)
y2=sample(x2, 120, replace = FALSE)
y3=sample(x3, 120, replace = FALSE)
y4=sample(x4, 120, replace = FALSE)
y5=sample(x5, 120, replace = FALSE)
c3=c(y1,y2,y3,y4,y5)
y1=sample(x1, 100, replace = FALSE)
y2=sample(x2, 100, replace = FALSE)
y3=sample(x3, 100, replace = FALSE)
y4=sample(x4, 100, replace = FALSE)
y5=sample(x5, 100, replace = FALSE)
y6=sample(x6, 100, replace = FALSE)
c4=c(y1,y2,y3,y4,y5,y6)
y1=sample(x1, 60, replace = FALSE)
y2=sample(x2, 60, replace = FALSE)
y3=sample(x3, 60, replace = FALSE)
y4=sample(x4, 60, replace = FALSE)
y5=sample(x5, 60, replace = FALSE)
y6=sample(x6, 60, replace = FALSE)
y7=sample(x7, 60, replace = FALSE)
y8=sample(x8, 60, replace = FALSE)
y9=sample(x9, 60, replace = FALSE)
y10=sample(x10, 60, replace = FALSE)
c5=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10)
y1=sample(x1, 50, replace = FALSE)
y2=sample(x2, 50, replace = FALSE)
y3=sample(x3, 50, replace = FALSE)
y4=sample(x4, 50, replace = FALSE)
y5=sample(x5, 50, replace = FALSE)
y6=sample(x6, 50, replace = FALSE)
y7=sample(x7, 50, replace = FALSE)
y8=sample(x8, 50, replace = FALSE)
y9=sample(x9, 50, replace = FALSE)
y10=sample(x10, 50, replace = FALSE)
y11=sample(x11, 50, replace = FALSE)
y12=sample(x12, 50, replace = FALSE)
c6=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12)
y1=sample(x1, 40, replace = FALSE)
y2=sample(x2, 40, replace = FALSE)
y3=sample(x3, 40, replace = FALSE)
y4=sample(x4, 40, replace = FALSE)
y5=sample(x5, 40, replace = FALSE)
y6=sample(x6, 40, replace = FALSE)
y7=sample(x7, 40, replace = FALSE)
y8=sample(x8, 40, replace = FALSE)
y9=sample(x9, 40, replace = FALSE)
y10=sample(x10, 40, replace = FALSE)
y11=sample(x11, 40, replace = FALSE)
y12=sample(x12, 40, replace = FALSE)
y13=sample(x13, 40, replace = FALSE)
y14=sample(x14, 40, replace = FALSE)
y15=sample(x15, 40, replace = FALSE)
c7=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15)
y1=sample(x1, 30, replace = FALSE)
y2=sample(x2, 30, replace = FALSE)
y3=sample(x3, 30, replace = FALSE)
y4=sample(x4, 30, replace = FALSE)
y5=sample(x5, 30, replace = FALSE)
y6=sample(x6, 30, replace = FALSE)
y7=sample(x7, 30, replace = FALSE)
y8=sample(x8, 30, replace = FALSE)
y9=sample(x9, 30, replace = FALSE)
y10=sample(x10, 30, replace = FALSE)
y11=sample(x11, 30, replace = FALSE)
y12=sample(x12, 30, replace = FALSE)
y13=sample(x13, 30, replace = FALSE)
y14=sample(x14, 30, replace = FALSE)
y15=sample(x15, 30, replace = FALSE)
y16=sample(x16, 30, replace = FALSE)
y17=sample(x17, 30, replace = FALSE)
y18=sample(x18, 30, replace = FALSE)
y19=sample(x19, 30, replace = FALSE)
y20=sample(x20, 30, replace = FALSE)
c8=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16,y17,y18,y19,y20)
t1=M*mean(c1); v1=M^2*(1-3/20)*var(c(mean(y1),mean(y2),mean(y3)))/3+M^2/3^2*sum(c(var(y1),var(y2),var(y3)))/200; v1x=M^2/3^2*sum(c(var(y1),var(y2),var(y3)))/200
t2=M*mean(c2); v2=M^2*(1-4/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4)))/4+M^2/4^2*sum(c(var(y1),var(y2),var(y3),var(y4)))/150;v2x=M^2/4^2*sum(c(var(y1),var(y2),var(y3),var(y4)))/150
t3=M*mean(c3); v3=M^2*(1-5/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5)))/5+M^2/5^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5)))/120;v3x=M^2/5^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5)))/120
t4=M*mean(c4); v4=M^2*(1-6/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6)))/6+M^2/6^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6)))/100; v4x=M^2/6^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6)))/100
t5=M*mean(c5); v5=M^2*(1-10/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10)))/10+M^2/10^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10)))/60;v5x=M^2/10^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10)))/60
t6=M*mean(c6); v6=M^2*(1-12/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12)))/12+M^2/12^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12)))/50;v6x=M^2/12^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12)))/50
t7=M*mean(c7); v7=M^2*(1-15/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12),mean(y13),mean(y14),mean(y15)))/15+M^2/15^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15)))/40;v7x=M^2/15^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15)))/40
t8=M*mean(c8); v8=M^2*(1-20/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12),mean(y13),mean(y14),mean(y15)))/15+M^2/20^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15),var(y16),var(y17),var(y18),var(y19),var(y20)))/30
cx7=cbind(rbind(n1=3, m1=200,t1,v1,v1x),rbind(n2=4,m2=150,t2,v2,v2x),rbind(n3=5,m3=120,t3,v3,v3x),rbind(n4=6,m4=100,t4,v4,v4x),rbind(n5=10,m6=60,t5,v5,v5x),rbind(n6=12,m6=50,t6,v6,v6x),rbind(n7=15,m7=40,t7,v7,v7x),rbind(n8=20,m8=30,t8,v8,v8))
y1=sample(x1, 200, replace = FALSE)
y2=sample(x2, 200, replace = FALSE)
y3=sample(x3, 200, replace = FALSE)
c1=c(y1,y2,y3)
y1=sample(x1, 150, replace = FALSE)
y2=sample(x2, 150, replace = FALSE)
y3=sample(x3, 150, replace = FALSE)
y4=sample(x4, 150, replace = FALSE)
c2=c(y1,y2,y3,y4)
y1=sample(x1, 120, replace = FALSE)
y2=sample(x2, 120, replace = FALSE)
y3=sample(x3, 120, replace = FALSE)
y4=sample(x4, 120, replace = FALSE)
y5=sample(x5, 120, replace = FALSE)
c3=c(y1,y2,y3,y4,y5)
y1=sample(x1, 100, replace = FALSE)
y2=sample(x2, 100, replace = FALSE)
y3=sample(x3, 100, replace = FALSE)
y4=sample(x4, 100, replace = FALSE)
y5=sample(x5, 100, replace = FALSE)
y6=sample(x6, 100, replace = FALSE)
c4=c(y1,y2,y3,y4,y5,y6)
y1=sample(x1, 60, replace = FALSE)
y2=sample(x2, 60, replace = FALSE)
y3=sample(x3, 60, replace = FALSE)
y4=sample(x4, 60, replace = FALSE)
y5=sample(x5, 60, replace = FALSE)
y6=sample(x6, 60, replace = FALSE)
y7=sample(x7, 60, replace = FALSE)
y8=sample(x8, 60, replace = FALSE)
y9=sample(x9, 60, replace = FALSE)
y10=sample(x10, 60, replace = FALSE)
c5=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10)
y1=sample(x1, 50, replace = FALSE)
y2=sample(x2, 50, replace = FALSE)
y3=sample(x3, 50, replace = FALSE)
y4=sample(x4, 50, replace = FALSE)
y5=sample(x5, 50, replace = FALSE)
y6=sample(x6, 50, replace = FALSE)
y7=sample(x7, 50, replace = FALSE)
y8=sample(x8, 50, replace = FALSE)
y9=sample(x9, 50, replace = FALSE)
y10=sample(x10, 50, replace = FALSE)
y11=sample(x11, 50, replace = FALSE)
y12=sample(x12, 50, replace = FALSE)
c6=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12)
y1=sample(x1, 40, replace = FALSE)
y2=sample(x2, 40, replace = FALSE)
y3=sample(x3, 40, replace = FALSE)
y4=sample(x4, 40, replace = FALSE)
y5=sample(x5, 40, replace = FALSE)
y6=sample(x6, 40, replace = FALSE)
y7=sample(x7, 40, replace = FALSE)
y8=sample(x8, 40, replace = FALSE)
y9=sample(x9, 40, replace = FALSE)
y10=sample(x10, 40, replace = FALSE)
y11=sample(x11, 40, replace = FALSE)
y12=sample(x12, 40, replace = FALSE)
y13=sample(x13, 40, replace = FALSE)
y14=sample(x14, 40, replace = FALSE)
y15=sample(x15, 40, replace = FALSE)
c7=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15)
y1=sample(x1, 30, replace = FALSE)
y2=sample(x2, 30, replace = FALSE)
y3=sample(x3, 30, replace = FALSE)
y4=sample(x4, 30, replace = FALSE)
y5=sample(x5, 30, replace = FALSE)
y6=sample(x6, 30, replace = FALSE)
y7=sample(x7, 30, replace = FALSE)
y8=sample(x8, 30, replace = FALSE)
y9=sample(x9, 30, replace = FALSE)
y10=sample(x10, 30, replace = FALSE)
y11=sample(x11, 30, replace = FALSE)
y12=sample(x12, 30, replace = FALSE)
y13=sample(x13, 30, replace = FALSE)
y14=sample(x14, 30, replace = FALSE)
y15=sample(x15, 30, replace = FALSE)
y16=sample(x16, 30, replace = FALSE)
y17=sample(x17, 30, replace = FALSE)
y18=sample(x18, 30, replace = FALSE)
y19=sample(x19, 30, replace = FALSE)
y20=sample(x20, 30, replace = FALSE)
c8=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16,y17,y18,y19,y20)
t1=M*mean(c1); v1=M^2*(1-3/20)*var(c(mean(y1),mean(y2),mean(y3)))/3+M^2/3^2*sum(c(var(y1),var(y2),var(y3)))/200; v1x=M^2/3^2*sum(c(var(y1),var(y2),var(y3)))/200
t2=M*mean(c2); v2=M^2*(1-4/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4)))/4+M^2/4^2*sum(c(var(y1),var(y2),var(y3),var(y4)))/150;v2x=M^2/4^2*sum(c(var(y1),var(y2),var(y3),var(y4)))/150
t3=M*mean(c3); v3=M^2*(1-5/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5)))/5+M^2/5^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5)))/120;v3x=M^2/5^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5)))/120
t4=M*mean(c4); v4=M^2*(1-6/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6)))/6+M^2/6^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6)))/100; v4x=M^2/6^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6)))/100
t5=M*mean(c5); v5=M^2*(1-10/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10)))/10+M^2/10^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10)))/60;v5x=M^2/10^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10)))/60
t6=M*mean(c6); v6=M^2*(1-12/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12)))/12+M^2/12^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12)))/50;v6x=M^2/12^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12)))/50
t7=M*mean(c7); v7=M^2*(1-15/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12),mean(y13),mean(y14),mean(y15)))/15+M^2/15^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15)))/40;v7x=M^2/15^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15)))/40
t8=M*mean(c8); v8=M^2*(1-20/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12),mean(y13),mean(y14),mean(y15)))/15+M^2/20^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15),var(y16),var(y17),var(y18),var(y19),var(y20)))/30
cx8=cbind(rbind(n1=3, m1=200,t1,v1,v1x),rbind(n2=4,m2=150,t2,v2,v2x),rbind(n3=5,m3=120,t3,v3,v3x),rbind(n4=6,m4=100,t4,v4,v4x),rbind(n5=10,m6=60,t5,v5,v5x),rbind(n6=12,m6=50,t6,v6,v6x),rbind(n7=15,m7=40,t7,v7,v7x),rbind(n8=20,m8=30,t8,v8,v8))
y1=sample(x1, 200, replace = FALSE)
y2=sample(x2, 200, replace = FALSE)
y3=sample(x3, 200, replace = FALSE)
c1=c(y1,y2,y3)
y1=sample(x1, 150, replace = FALSE)
y2=sample(x2, 150, replace = FALSE)
y3=sample(x3, 150, replace = FALSE)
y4=sample(x4, 150, replace = FALSE)
c2=c(y1,y2,y3,y4)
y1=sample(x1, 120, replace = FALSE)
y2=sample(x2, 120, replace = FALSE)
y3=sample(x3, 120, replace = FALSE)
y4=sample(x4, 120, replace = FALSE)
y5=sample(x5, 120, replace = FALSE)
c3=c(y1,y2,y3,y4,y5)
y1=sample(x1, 100, replace = FALSE)
y2=sample(x2, 100, replace = FALSE)
y3=sample(x3, 100, replace = FALSE)
y4=sample(x4, 100, replace = FALSE)
y5=sample(x5, 100, replace = FALSE)
y6=sample(x6, 100, replace = FALSE)
c4=c(y1,y2,y3,y4,y5,y6)
y1=sample(x1, 60, replace = FALSE)
y2=sample(x2, 60, replace = FALSE)
y3=sample(x3, 60, replace = FALSE)
y4=sample(x4, 60, replace = FALSE)
y5=sample(x5, 60, replace = FALSE)
y6=sample(x6, 60, replace = FALSE)
y7=sample(x7, 60, replace = FALSE)
y8=sample(x8, 60, replace = FALSE)
y9=sample(x9, 60, replace = FALSE)
y10=sample(x10, 60, replace = FALSE)
c5=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10)
y1=sample(x1, 50, replace = FALSE)
y2=sample(x2, 50, replace = FALSE)
y3=sample(x3, 50, replace = FALSE)
y4=sample(x4, 50, replace = FALSE)
y5=sample(x5, 50, replace = FALSE)
y6=sample(x6, 50, replace = FALSE)
y7=sample(x7, 50, replace = FALSE)
y8=sample(x8, 50, replace = FALSE)
y9=sample(x9, 50, replace = FALSE)
y10=sample(x10, 50, replace = FALSE)
y11=sample(x11, 50, replace = FALSE)
y12=sample(x12, 50, replace = FALSE)
c6=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12)
y1=sample(x1, 40, replace = FALSE)
y2=sample(x2, 40, replace = FALSE)
y3=sample(x3, 40, replace = FALSE)
y4=sample(x4, 40, replace = FALSE)
y5=sample(x5, 40, replace = FALSE)
y6=sample(x6, 40, replace = FALSE)
y7=sample(x7, 40, replace = FALSE)
y8=sample(x8, 40, replace = FALSE)
y9=sample(x9, 40, replace = FALSE)
y10=sample(x10, 40, replace = FALSE)
y11=sample(x11, 40, replace = FALSE)
y12=sample(x12, 40, replace = FALSE)
y13=sample(x13, 40, replace = FALSE)
y14=sample(x14, 40, replace = FALSE)
y15=sample(x15, 40, replace = FALSE)
c7=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15)
y1=sample(x1, 30, replace = FALSE)
y2=sample(x2, 30, replace = FALSE)
y3=sample(x3, 30, replace = FALSE)
y4=sample(x4, 30, replace = FALSE)
y5=sample(x5, 30, replace = FALSE)
y6=sample(x6, 30, replace = FALSE)
y7=sample(x7, 30, replace = FALSE)
y8=sample(x8, 30, replace = FALSE)
y9=sample(x9, 30, replace = FALSE)
y10=sample(x10, 30, replace = FALSE)
y11=sample(x11, 30, replace = FALSE)
y12=sample(x12, 30, replace = FALSE)
y13=sample(x13, 30, replace = FALSE)
y14=sample(x14, 30, replace = FALSE)
y15=sample(x15, 30, replace = FALSE)
y16=sample(x16, 30, replace = FALSE)
y17=sample(x17, 30, replace = FALSE)
y18=sample(x18, 30, replace = FALSE)
y19=sample(x19, 30, replace = FALSE)
y20=sample(x20, 30, replace = FALSE)
c8=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16,y17,y18,y19,y20)
t1=M*mean(c1); v1=M^2*(1-3/20)*var(c(mean(y1),mean(y2),mean(y3)))/3+M^2/3^2*sum(c(var(y1),var(y2),var(y3)))/200; v1x=M^2/3^2*sum(c(var(y1),var(y2),var(y3)))/200
t2=M*mean(c2); v2=M^2*(1-4/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4)))/4+M^2/4^2*sum(c(var(y1),var(y2),var(y3),var(y4)))/150;v2x=M^2/4^2*sum(c(var(y1),var(y2),var(y3),var(y4)))/150
t3=M*mean(c3); v3=M^2*(1-5/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5)))/5+M^2/5^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5)))/120;v3x=M^2/5^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5)))/120
t4=M*mean(c4); v4=M^2*(1-6/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6)))/6+M^2/6^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6)))/100; v4x=M^2/6^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6)))/100
t5=M*mean(c5); v5=M^2*(1-10/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10)))/10+M^2/10^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10)))/60;v5x=M^2/10^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10)))/60
t6=M*mean(c6); v6=M^2*(1-12/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12)))/12+M^2/12^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12)))/50;v6x=M^2/12^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12)))/50
t7=M*mean(c7); v7=M^2*(1-15/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12),mean(y13),mean(y14),mean(y15)))/15+M^2/15^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15)))/40;v7x=M^2/15^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15)))/40
t8=M*mean(c8); v8=M^2*(1-20/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12),mean(y13),mean(y14),mean(y15)))/15+M^2/20^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15),var(y16),var(y17),var(y18),var(y19),var(y20)))/30
cx9=cbind(rbind(n1=3, m1=200,t1,v1,v1x),rbind(n2=4,m2=150,t2,v2,v2x),rbind(n3=5,m3=120,t3,v3,v3x),rbind(n4=6,m4=100,t4,v4,v4x),rbind(n5=10,m6=60,t5,v5,v5x),rbind(n6=12,m6=50,t6,v6,v6x),rbind(n7=15,m7=40,t7,v7,v7x),rbind(n8=20,m8=30,t8,v8,v8))
y1=sample(x1, 200, replace = FALSE)
y2=sample(x2, 200, replace = FALSE)
y3=sample(x3, 200, replace = FALSE)
c1=c(y1,y2,y3)
y1=sample(x1, 150, replace = FALSE)
y2=sample(x2, 150, replace = FALSE)
y3=sample(x3, 150, replace = FALSE)
y4=sample(x4, 150, replace = FALSE)
c2=c(y1,y2,y3,y4)
y1=sample(x1, 120, replace = FALSE)
y2=sample(x2, 120, replace = FALSE)
y3=sample(x3, 120, replace = FALSE)
y4=sample(x4, 120, replace = FALSE)
y5=sample(x5, 120, replace = FALSE)
c3=c(y1,y2,y3,y4,y5)
y1=sample(x1, 100, replace = FALSE)
y2=sample(x2, 100, replace = FALSE)
y3=sample(x3, 100, replace = FALSE)
y4=sample(x4, 100, replace = FALSE)
y5=sample(x5, 100, replace = FALSE)
y6=sample(x6, 100, replace = FALSE)
c4=c(y1,y2,y3,y4,y5,y6)
y1=sample(x1, 60, replace = FALSE)
y2=sample(x2, 60, replace = FALSE)
y3=sample(x3, 60, replace = FALSE)
y4=sample(x4, 60, replace = FALSE)
y5=sample(x5, 60, replace = FALSE)
y6=sample(x6, 60, replace = FALSE)
y7=sample(x7, 60, replace = FALSE)
y8=sample(x8, 60, replace = FALSE)
y9=sample(x9, 60, replace = FALSE)
y10=sample(x10, 60, replace = FALSE)
c5=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10)
y1=sample(x1, 50, replace = FALSE)
y2=sample(x2, 50, replace = FALSE)
y3=sample(x3, 50, replace = FALSE)
y4=sample(x4, 50, replace = FALSE)
y5=sample(x5, 50, replace = FALSE)
y6=sample(x6, 50, replace = FALSE)
y7=sample(x7, 50, replace = FALSE)
y8=sample(x8, 50, replace = FALSE)
y9=sample(x9, 50, replace = FALSE)
y10=sample(x10, 50, replace = FALSE)
y11=sample(x11, 50, replace = FALSE)
y12=sample(x12, 50, replace = FALSE)
c6=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12)
y1=sample(x1, 40, replace = FALSE)
y2=sample(x2, 40, replace = FALSE)
y3=sample(x3, 40, replace = FALSE)
y4=sample(x4, 40, replace = FALSE)
y5=sample(x5, 40, replace = FALSE)
y6=sample(x6, 40, replace = FALSE)
y7=sample(x7, 40, replace = FALSE)
y8=sample(x8, 40, replace = FALSE)
y9=sample(x9, 40, replace = FALSE)
y10=sample(x10, 40, replace = FALSE)
y11=sample(x11, 40, replace = FALSE)
y12=sample(x12, 40, replace = FALSE)
y13=sample(x13, 40, replace = FALSE)
y14=sample(x14, 40, replace = FALSE)
y15=sample(x15, 40, replace = FALSE)
c7=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15)
y1=sample(x1, 30, replace = FALSE)
y2=sample(x2, 30, replace = FALSE)
y3=sample(x3, 30, replace = FALSE)
y4=sample(x4, 30, replace = FALSE)
y5=sample(x5, 30, replace = FALSE)
y6=sample(x6, 30, replace = FALSE)
y7=sample(x7, 30, replace = FALSE)
y8=sample(x8, 30, replace = FALSE)
y9=sample(x9, 30, replace = FALSE)
y10=sample(x10, 30, replace = FALSE)
y11=sample(x11, 30, replace = FALSE)
y12=sample(x12, 30, replace = FALSE)
y13=sample(x13, 30, replace = FALSE)
y14=sample(x14, 30, replace = FALSE)
y15=sample(x15, 30, replace = FALSE)
y16=sample(x16, 30, replace = FALSE)
y17=sample(x17, 30, replace = FALSE)
y18=sample(x18, 30, replace = FALSE)
y19=sample(x19, 30, replace = FALSE)
y20=sample(x20, 30, replace = FALSE)
c8=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16,y17,y18,y19,y20)
t1=M*mean(c1); v1=M^2*(1-3/20)*var(c(mean(y1),mean(y2),mean(y3)))/3+M^2/3^2*sum(c(var(y1),var(y2),var(y3)))/200; v1x=M^2/3^2*sum(c(var(y1),var(y2),var(y3)))/200
t2=M*mean(c2); v2=M^2*(1-4/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4)))/4+M^2/4^2*sum(c(var(y1),var(y2),var(y3),var(y4)))/150;v2x=M^2/4^2*sum(c(var(y1),var(y2),var(y3),var(y4)))/150
t3=M*mean(c3); v3=M^2*(1-5/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5)))/5+M^2/5^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5)))/120;v3x=M^2/5^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5)))/120
t4=M*mean(c4); v4=M^2*(1-6/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6)))/6+M^2/6^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6)))/100; v4x=M^2/6^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6)))/100
t5=M*mean(c5); v5=M^2*(1-10/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10)))/10+M^2/10^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10)))/60;v5x=M^2/10^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10)))/60
t6=M*mean(c6); v6=M^2*(1-12/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12)))/12+M^2/12^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12)))/50;v6x=M^2/12^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12)))/50
t7=M*mean(c7); v7=M^2*(1-15/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12),mean(y13),mean(y14),mean(y15)))/15+M^2/15^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15)))/40;v7x=M^2/15^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15)))/40
t8=M*mean(c8); v8=M^2*(1-20/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12),mean(y13),mean(y14),mean(y15)))/15+M^2/20^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15),var(y16),var(y17),var(y18),var(y19),var(y20)))/30
cx10=cbind(rbind(n1=3, m1=200,t1,v1,v1x),rbind(n2=4,m2=150,t2,v2,v2x),rbind(n3=5,m3=120,t3,v3,v3x),rbind(n4=6,m4=100,t4,v4,v4x),rbind(n5=10,m6=60,t5,v5,v5x),rbind(n6=12,m6=50,t6,v6,v6x),rbind(n7=15,m7=40,t7,v7,v7x),rbind(n8=20,m8=30,t8,v8,v8))
y1=sample(x1, 200, replace = FALSE)
y2=sample(x2, 200, replace = FALSE)
y3=sample(x3, 200, replace = FALSE)
c1=c(y1,y2,y3)
y1=sample(x1, 150, replace = FALSE)
y2=sample(x2, 150, replace = FALSE)
y3=sample(x3, 150, replace = FALSE)
y4=sample(x4, 150, replace = FALSE)
c2=c(y1,y2,y3,y4)
y1=sample(x1, 120, replace = FALSE)
y2=sample(x2, 120, replace = FALSE)
y3=sample(x3, 120, replace = FALSE)
y4=sample(x4, 120, replace = FALSE)
y5=sample(x5, 120, replace = FALSE)
c3=c(y1,y2,y3,y4,y5)
y1=sample(x1, 100, replace = FALSE)
y2=sample(x2, 100, replace = FALSE)
y3=sample(x3, 100, replace = FALSE)
y4=sample(x4, 100, replace = FALSE)
y5=sample(x5, 100, replace = FALSE)
y6=sample(x6, 100, replace = FALSE)
c4=c(y1,y2,y3,y4,y5,y6)
y1=sample(x1, 60, replace = FALSE)
y2=sample(x2, 60, replace = FALSE)
y3=sample(x3, 60, replace = FALSE)
y4=sample(x4, 60, replace = FALSE)
y5=sample(x5, 60, replace = FALSE)
y6=sample(x6, 60, replace = FALSE)
y7=sample(x7, 60, replace = FALSE)
y8=sample(x8, 60, replace = FALSE)
y9=sample(x9, 60, replace = FALSE)
y10=sample(x10, 60, replace = FALSE)
c5=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10)
y1=sample(x1, 50, replace = FALSE)
y2=sample(x2, 50, replace = FALSE)
y3=sample(x3, 50, replace = FALSE)
y4=sample(x4, 50, replace = FALSE)
y5=sample(x5, 50, replace = FALSE)
y6=sample(x6, 50, replace = FALSE)
y7=sample(x7, 50, replace = FALSE)
y8=sample(x8, 50, replace = FALSE)
y9=sample(x9, 50, replace = FALSE)
y10=sample(x10, 50, replace = FALSE)
y11=sample(x11, 50, replace = FALSE)
y12=sample(x12, 50, replace = FALSE)
c6=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12)
y1=sample(x1, 40, replace = FALSE)
y2=sample(x2, 40, replace = FALSE)
y3=sample(x3, 40, replace = FALSE)
y4=sample(x4, 40, replace = FALSE)
y5=sample(x5, 40, replace = FALSE)
y6=sample(x6, 40, replace = FALSE)
y7=sample(x7, 40, replace = FALSE)
y8=sample(x8, 40, replace = FALSE)
y9=sample(x9, 40, replace = FALSE)
y10=sample(x10, 40, replace = FALSE)
y11=sample(x11, 40, replace = FALSE)
y12=sample(x12, 40, replace = FALSE)
y13=sample(x13, 40, replace = FALSE)
y14=sample(x14, 40, replace = FALSE)
y15=sample(x15, 40, replace = FALSE)
c7=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15)
y1=sample(x1, 30, replace = FALSE)
y2=sample(x2, 30, replace = FALSE)
y3=sample(x3, 30, replace = FALSE)
y4=sample(x4, 30, replace = FALSE)
y5=sample(x5, 30, replace = FALSE)
y6=sample(x6, 30, replace = FALSE)
y7=sample(x7, 30, replace = FALSE)
y8=sample(x8, 30, replace = FALSE)
y9=sample(x9, 30, replace = FALSE)
y10=sample(x10, 30, replace = FALSE)
y11=sample(x11, 30, replace = FALSE)
y12=sample(x12, 30, replace = FALSE)
y13=sample(x13, 30, replace = FALSE)
y14=sample(x14, 30, replace = FALSE)
y15=sample(x15, 30, replace = FALSE)
y16=sample(x16, 30, replace = FALSE)
y17=sample(x17, 30, replace = FALSE)
y18=sample(x18, 30, replace = FALSE)
y19=sample(x19, 30, replace = FALSE)
y20=sample(x20, 30, replace = FALSE)
c8=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16,y17,y18,y19,y20)
t1=M*mean(c1); v1=M^2*(1-3/20)*var(c(mean(y1),mean(y2),mean(y3)))/3+M^2/3^2*sum(c(var(y1),var(y2),var(y3)))/200; v1x=M^2/3^2*sum(c(var(y1),var(y2),var(y3)))/200
t2=M*mean(c2); v2=M^2*(1-4/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4)))/4+M^2/4^2*sum(c(var(y1),var(y2),var(y3),var(y4)))/150;v2x=M^2/4^2*sum(c(var(y1),var(y2),var(y3),var(y4)))/150
t3=M*mean(c3); v3=M^2*(1-5/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5)))/5+M^2/5^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5)))/120;v3x=M^2/5^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5)))/120
t4=M*mean(c4); v4=M^2*(1-6/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6)))/6+M^2/6^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6)))/100; v4x=M^2/6^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6)))/100
t5=M*mean(c5); v5=M^2*(1-10/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10)))/10+M^2/10^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10)))/60;v5x=M^2/10^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10)))/60
t6=M*mean(c6); v6=M^2*(1-12/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12)))/12+M^2/12^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12)))/50;v6x=M^2/12^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12)))/50
t7=M*mean(c7); v7=M^2*(1-15/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12),mean(y13),mean(y14),mean(y15)))/15+M^2/15^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15)))/40;v7x=M^2/15^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15)))/40
t8=M*mean(c8); v8=M^2*(1-20/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12),mean(y13),mean(y14),mean(y15)))/15+M^2/20^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15),var(y16),var(y17),var(y18),var(y19),var(y20)))/30
cx11=cbind(rbind(n1=3, m1=200,t1,v1,v1x),rbind(n2=4,m2=150,t2,v2,v2x),rbind(n3=5,m3=120,t3,v3,v3x),rbind(n4=6,m4=100,t4,v4,v4x),rbind(n5=10,m6=60,t5,v5,v5x),rbind(n6=12,m6=50,t6,v6,v6x),rbind(n7=15,m7=40,t7,v7,v7x),rbind(n8=20,m8=30,t8,v8,v8))
y1=sample(x1, 200, replace = FALSE)
y2=sample(x2, 200, replace = FALSE)
y3=sample(x3, 200, replace = FALSE)
c1=c(y1,y2,y3)
y1=sample(x1, 150, replace = FALSE)
y2=sample(x2, 150, replace = FALSE)
y3=sample(x3, 150, replace = FALSE)
y4=sample(x4, 150, replace = FALSE)
c2=c(y1,y2,y3,y4)
y1=sample(x1, 120, replace = FALSE)
y2=sample(x2, 120, replace = FALSE)
y3=sample(x3, 120, replace = FALSE)
y4=sample(x4, 120, replace = FALSE)
y5=sample(x5, 120, replace = FALSE)
c3=c(y1,y2,y3,y4,y5)
y1=sample(x1, 100, replace = FALSE)
y2=sample(x2, 100, replace = FALSE)
y3=sample(x3, 100, replace = FALSE)
y4=sample(x4, 100, replace = FALSE)
y5=sample(x5, 100, replace = FALSE)
y6=sample(x6, 100, replace = FALSE)
c4=c(y1,y2,y3,y4,y5,y6)
y1=sample(x1, 60, replace = FALSE)
y2=sample(x2, 60, replace = FALSE)
y3=sample(x3, 60, replace = FALSE)
y4=sample(x4, 60, replace = FALSE)
y5=sample(x5, 60, replace = FALSE)
y6=sample(x6, 60, replace = FALSE)
y7=sample(x7, 60, replace = FALSE)
y8=sample(x8, 60, replace = FALSE)
y9=sample(x9, 60, replace = FALSE)
y10=sample(x10, 60, replace = FALSE)
c5=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10)
y1=sample(x1, 50, replace = FALSE)
y2=sample(x2, 50, replace = FALSE)
y3=sample(x3, 50, replace = FALSE)
y4=sample(x4, 50, replace = FALSE)
y5=sample(x5, 50, replace = FALSE)
y6=sample(x6, 50, replace = FALSE)
y7=sample(x7, 50, replace = FALSE)
y8=sample(x8, 50, replace = FALSE)
y9=sample(x9, 50, replace = FALSE)
y10=sample(x10, 50, replace = FALSE)
y11=sample(x11, 50, replace = FALSE)
y12=sample(x12, 50, replace = FALSE)
c6=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12)
y1=sample(x1, 40, replace = FALSE)
y2=sample(x2, 40, replace = FALSE)
y3=sample(x3, 40, replace = FALSE)
y4=sample(x4, 40, replace = FALSE)
y5=sample(x5, 40, replace = FALSE)
y6=sample(x6, 40, replace = FALSE)
y7=sample(x7, 40, replace = FALSE)
y8=sample(x8, 40, replace = FALSE)
y9=sample(x9, 40, replace = FALSE)
y10=sample(x10, 40, replace = FALSE)
y11=sample(x11, 40, replace = FALSE)
y12=sample(x12, 40, replace = FALSE)
y13=sample(x13, 40, replace = FALSE)
y14=sample(x14, 40, replace = FALSE)
y15=sample(x15, 40, replace = FALSE)
c7=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15)
y1=sample(x1, 30, replace = FALSE)
y2=sample(x2, 30, replace = FALSE)
y3=sample(x3, 30, replace = FALSE)
y4=sample(x4, 30, replace = FALSE)
y5=sample(x5, 30, replace = FALSE)
y6=sample(x6, 30, replace = FALSE)
y7=sample(x7, 30, replace = FALSE)
y8=sample(x8, 30, replace = FALSE)
y9=sample(x9, 30, replace = FALSE)
y10=sample(x10, 30, replace = FALSE)
y11=sample(x11, 30, replace = FALSE)
y12=sample(x12, 30, replace = FALSE)
y13=sample(x13, 30, replace = FALSE)
y14=sample(x14, 30, replace = FALSE)
y15=sample(x15, 30, replace = FALSE)
y16=sample(x16, 30, replace = FALSE)
y17=sample(x17, 30, replace = FALSE)
y18=sample(x18, 30, replace = FALSE)
y19=sample(x19, 30, replace = FALSE)
y20=sample(x20, 30, replace = FALSE)
c8=c(y1,y2,y3,y4,y5,y6,y7,y8,y9,y10,y11,y12,y13,y14,y15,y16,y17,y18,y19,y20)
t1=M*mean(c1); v1=M^2*(1-3/20)*var(c(mean(y1),mean(y2),mean(y3)))/3+M^2/3^2*sum(c(var(y1),var(y2),var(y3)))/200; v1x=M^2/3^2*sum(c(var(y1),var(y2),var(y3)))/200
t2=M*mean(c2); v2=M^2*(1-4/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4)))/4+M^2/4^2*sum(c(var(y1),var(y2),var(y3),var(y4)))/150;v2x=M^2/4^2*sum(c(var(y1),var(y2),var(y3),var(y4)))/150
t3=M*mean(c3); v3=M^2*(1-5/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5)))/5+M^2/5^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5)))/120;v3x=M^2/5^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5)))/120
t4=M*mean(c4); v4=M^2*(1-6/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6)))/6+M^2/6^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6)))/100; v4x=M^2/6^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6)))/100
t5=M*mean(c5); v5=M^2*(1-10/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10)))/10+M^2/10^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10)))/60;v5x=M^2/10^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10)))/60
t6=M*mean(c6); v6=M^2*(1-12/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12)))/12+M^2/12^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12)))/50;v6x=M^2/12^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12)))/50
t7=M*mean(c7); v7=M^2*(1-15/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12),mean(y13),mean(y14),mean(y15)))/15+M^2/15^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15)))/40;v7x=M^2/15^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15)))/40
t8=M*mean(c8); v8=M^2*(1-20/20)*var(c(mean(y1),mean(y2),mean(y3),mean(y4),mean(y5),mean(y6),mean(y7),mean(y8),mean(y9),mean(y10),mean(y11),mean(y12),mean(y13),mean(y14),mean(y15)))/15+M^2/20^2*sum(c(var(y1),var(y2),var(y3),var(y4),var(y5),var(y6),var(y7),var(y8),var(y9),var(y10),var(y11),var(y12),var(y13),var(y14),var(y15),var(y16),var(y17),var(y18),var(y19),var(y20)))/30
cx12=cbind(rbind(n1=3, m1=200,t1,v1,v1x),rbind(n2=4,m2=150,t2,v2,v2x),rbind(n3=5,m3=120,t3,v3,v3x),rbind(n4=6,m4=100,t4,v4,v4x),rbind(n5=10,m6=60,t5,v5,v5x),rbind(n6=12,m6=50,t6,v6,v6x),rbind(n7=15,m7=40,t7,v7,v7x),rbind(n8=20,m8=30,t8,v8,v8))
cxx1=cbind(cx1,cx2,cx3,cx4,cx5,cx6,cx7,cx8,cx9,cx10,cx11,cx12)
cbind(cxx1,apply(cxx1,1,mean),apply(cxx1,1, var))## [,1] [,2] [,3] [,4] [,5]
## n1 3.000000e+00 4.000000e+00 5.000000e+00 6.000000e+00 1.000000e+01
## m1 2.000000e+02 1.500000e+02 1.200000e+02 1.000000e+02 6.000000e+01
## t1 1.910482e+07 1.858920e+07 2.134746e+07 1.565491e+07 1.893237e+07
## v1 5.044986e+12 3.508151e+12 3.409788e+12 2.926547e+12 3.743120e+12
## v1x 5.833231e+11 1.166402e+12 1.361578e+12 1.350482e+12 1.039366e+12
## [,6] [,7] [,8] [,9] [,10]
## n1 1.200000e+01 1.500000e+01 2.000000e+01 3.000000e+00 4.000000e+00
## m1 5.000000e+01 4.000000e+01 3.000000e+01 2.000000e+02 1.500000e+02
## t1 2.071719e+07 1.803388e+07 1.691416e+07 1.838008e+07 1.760553e+07
## v1 3.109289e+12 2.050838e+12 1.197613e+12 1.530838e+12 1.705000e+13
## v1x 1.442444e+12 1.282017e+12 1.197613e+12 1.060206e+12 2.720621e+12
## [,11] [,12] [,13] [,14] [,15]
## n1 5.000000e+00 6.000000e+00 1.000000e+01 1.200000e+01 1.500000e+01
## m1 1.200000e+02 1.000000e+02 6.000000e+01 5.000000e+01 4.000000e+01
## t1 1.712322e+07 1.745779e+07 1.902165e+07 1.535942e+07 1.728105e+07
## v1 5.431632e+13 3.923387e+13 1.852944e+13 1.273560e+13 7.914731e+12
## v1x 1.167718e+13 9.938791e+12 7.295194e+12 6.486184e+12 5.429058e+12
## [,16] [,17] [,18] [,19] [,20]
## n1 2.000000e+01 3.000000e+00 4.000000e+00 5.000000e+00 6.000000e+00
## m1 3.000000e+01 2.000000e+02 1.500000e+02 1.200000e+02 1.000000e+02
## t1 2.222924e+07 1.953740e+07 1.998006e+07 1.911675e+07 1.947094e+07
## v1 4.369369e+12 2.336142e+12 5.628650e+13 4.153787e+13 3.090213e+13
## v1x 4.369369e+12 9.876796e+11 2.630690e+13 2.166940e+13 1.853764e+13
## [,21] [,22] [,23] [,24] [,25]
## n1 1.000000e+01 1.200000e+01 1.500000e+01 2.000000e+01 3.000000e+00
## m1 6.000000e+01 5.000000e+01 4.000000e+01 3.000000e+01 2.000000e+02
## t1 2.056020e+07 2.049217e+07 1.946389e+07 2.058814e+07 1.866503e+07
## v1 1.750232e+13 1.474988e+13 1.060414e+13 7.065682e+12 3.761007e+13
## v1x 1.320508e+13 1.127815e+13 9.217187e+12 7.065682e+12 1.079804e+12
## [,26] [,27] [,28] [,29] [,30]
## n1 4.000000e+00 5.000000e+00 6.000000e+00 1.000000e+01 1.200000e+01
## m1 1.500000e+02 1.200000e+02 1.000000e+02 6.000000e+01 5.000000e+01
## t1 1.873269e+07 1.788603e+07 1.720052e+07 1.614851e+07 1.713885e+07
## v1 2.876771e+13 1.826958e+13 1.349287e+13 9.699625e+12 7.465941e+12
## v1x 8.887064e+11 2.230468e+12 2.206596e+12 3.464780e+12 3.207713e+12
## [,31] [,32] [,33] [,34] [,35]
## n1 1.500000e+01 2.000000e+01 3.000000e+00 4.000000e+00 5.000000e+00
## m1 4.000000e+01 3.000000e+01 2.000000e+02 1.500000e+02 1.200000e+02
## t1 1.890823e+07 1.886915e+07 1.833388e+07 1.992007e+07 2.122453e+07
## v1 4.443748e+12 2.471348e+12 8.225588e+12 5.648988e+12 6.105289e+12
## v1x 2.739435e+12 2.471348e+12 6.439532e+11 1.913597e+12 1.931374e+12
## [,36] [,37] [,38] [,39] [,40]
## n1 6.000000e+00 1.000000e+01 1.200000e+01 1.500000e+01 2.000000e+01
## m1 1.000000e+02 6.000000e+01 5.000000e+01 4.000000e+01 3.000000e+01
## t1 1.646835e+07 1.404344e+07 1.927204e+07 1.747119e+07 2.231502e+07
## v1 6.862996e+12 1.251132e+13 9.298266e+12 6.174442e+12 3.725324e+12
## v1x 2.409506e+12 6.002826e+12 5.658302e+12 4.617747e+12 3.725324e+12
## [,41] [,42] [,43] [,44] [,45]
## n1 3 4.000000e+00 5.000000e+00 6.000000e+00 1.000000e+01
## m1 200 1.500000e+02 1.200000e+02 1.000000e+02 6.000000e+01
## t1 20561363 2.277595e+07 2.249822e+07 1.987778e+07 2.284483e+07
## v1 755734597650 1.389408e+13 1.020217e+13 8.150023e+12 5.801677e+12
## v1x 634229133965 5.436920e+12 5.439214e+12 4.608452e+12 3.413484e+12
## [,46] [,47] [,48] [,49] [,50]
## n1 1.200000e+01 1.500000e+01 2.000000e+01 3.000000e+00 4.000000e+00
## m1 5.000000e+01 4.000000e+01 3.000000e+01 2.000000e+02 1.500000e+02
## t1 2.254041e+07 1.846617e+07 1.736628e+07 1.717349e+07 1.990346e+07
## v1 4.393645e+12 3.138650e+12 2.136098e+12 5.376118e+12 8.905508e+12
## v1x 3.048375e+12 2.593216e+12 2.136098e+12 5.107818e+11 3.732430e+12
## [,51] [,52] [,53] [,54] [,55]
## n1 5.000000e+00 6.000000e+00 1.000000e+01 1.200000e+01 1.500000e+01
## m1 1.200000e+02 1.000000e+02 6.000000e+01 5.000000e+01 4.000000e+01
## t1 1.789570e+07 2.065408e+07 2.226341e+07 1.872309e+07 2.370742e+07
## v1 1.494900e+13 1.155535e+13 8.787260e+12 7.564725e+12 5.113342e+12
## v1x 2.999914e+12 2.735857e+12 4.488922e+12 4.664674e+12 3.904000e+12
## [,56] [,57] [,58] [,59] [,60]
## n1 2.000000e+01 3.000000e+00 4.000000e+00 5.000000e+00 6.000000e+00
## m1 3.000000e+01 2.000000e+02 1.500000e+02 1.200000e+02 1.000000e+02
## t1 1.857139e+07 1.664013e+07 1.826857e+07 1.998512e+07 1.932571e+07
## v1 3.222493e+12 3.667955e+12 3.406458e+12 5.639739e+12 4.494978e+12
## v1x 3.222493e+12 7.571222e+11 1.288922e+12 2.315611e+12 2.118276e+12
## [,61] [,62] [,63] [,64] [,65]
## n1 1.000000e+01 1.200000e+01 1.500000e+01 2.000000e+01 3.000000e+00
## m1 6.000000e+01 5.000000e+01 4.000000e+01 3.000000e+01 2.000000e+02
## t1 2.041820e+07 1.843134e+07 2.143906e+07 1.926809e+07 1.983268e+07
## v1 4.711031e+12 4.769538e+12 3.273499e+12 1.942340e+12 3.483778e+12
## v1x 1.609742e+12 2.355206e+12 2.127519e+12 1.942340e+12 7.999044e+11
## [,66] [,67] [,68] [,69] [,70]
## n1 4.000000e+00 5.000000e+00 6.000000e+00 1.000000e+01 1.200000e+01
## m1 1.500000e+02 1.200000e+02 1.000000e+02 6.000000e+01 5.000000e+01
## t1 1.694163e+07 1.849618e+07 1.862369e+07 2.112496e+07 1.614795e+07
## v1 1.662954e+13 1.310227e+13 8.530307e+12 4.432222e+12 9.225544e+12
## v1x 6.613007e+11 6.551558e+11 6.665526e+11 1.507938e+12 4.337761e+12
## [,71] [,72] [,73] [,74] [,75]
## n1 1.500000e+01 2.000000e+01 3.000000e+00 4.000000e+00 5.000000e+00
## m1 4.000000e+01 3.000000e+01 2.000000e+02 1.500000e+02 1.200000e+02
## t1 1.613388e+07 1.782515e+07 1.893530e+07 1.982845e+07 1.949752e+07
## v1 5.621185e+12 2.956463e+12 1.106389e+12 2.512909e+12 9.327684e+12
## v1x 3.627440e+12 2.956463e+12 7.324374e+11 1.154614e+12 2.652963e+12
## [,76] [,77] [,78] [,79] [,80]
## n1 6.000000e+00 1.000000e+01 1.200000e+01 1.500000e+01 2.000000e+01
## m1 1.000000e+02 6.000000e+01 5.000000e+01 4.000000e+01 3.000000e+01
## t1 1.904096e+07 1.635072e+07 2.039758e+07 2.139000e+07 2.048262e+07
## v1 6.556146e+12 8.015593e+12 6.985591e+12 5.173763e+12 3.720330e+12
## v1x 2.372020e+12 6.248475e+12 5.455320e+12 4.524410e+12 3.720330e+12
## [,81] [,82] [,83] [,84] [,85]
## n1 3.000000e+00 4.000000e+00 5.000000e+00 6.000000e+00 1.000000e+01
## m1 2.000000e+02 1.500000e+02 1.200000e+02 1.000000e+02 6.000000e+01
## t1 1.767023e+07 1.810693e+07 1.711805e+07 1.822963e+07 1.953832e+07
## v1 1.443096e+12 3.413278e+12 6.994480e+12 7.027454e+12 8.464293e+12
## v1x 4.632361e+11 2.860310e+12 2.394944e+12 2.222369e+12 4.721455e+12
## [,86] [,87] [,88] [,89] [,90]
## n1 1.200000e+01 1.500000e+01 2.000000e+01 3.000000e+00 4.000000e+00
## m1 5.000000e+01 4.000000e+01 3.000000e+01 2.000000e+02 1.500000e+02
## t1 1.722219e+07 1.712968e+07 1.733703e+07 1.883447e+07 1.849318e+07
## v1 6.666597e+12 4.366357e+12 2.669747e+12 5.284806e+12 5.071352e+12
## v1x 3.976072e+12 3.258990e+12 2.669747e+12 6.219923e+11 1.375672e+12
## [,91] [,92] [,93] [,94] [,95]
## n1 5.000000e+00 6.000000e+00 1.000000e+01 1.200000e+01 1.500000e+01
## m1 1.200000e+02 1.000000e+02 6.000000e+01 5.000000e+01 4.000000e+01
## t1 2.187966e+07 1.810554e+07 2.232842e+07 2.053703e+07 1.991900e+07
## v1 1.584626e+13 1.169552e+13 7.928733e+12 7.301591e+12 5.235159e+12
## v1x 7.708812e+12 6.543845e+12 4.835027e+12 5.351530e+12 4.410051e+12
## [,96] [,97] [,98]
## n1 2.000000e+01 9.375000e+00 3.181579e+01
## m1 3.000000e+01 9.375000e+01 3.181579e+03
## t1 2.003773e+07 1.904890e+07 3.566018e+12
## v1 3.578385e+12 9.360901e+12 1.055116e+26
## v1x 3.578385e+12 3.948004e+12 1.764340e+2510000/c(a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15,a16,a17,a18,a19,a20)## [1] 16666.67 17241.38 11363.64 166666.67 125000.00 18518.52 125000.00
## [8] 83333.33 26315.79 500000.00 25000.00 83333.33 11111.11 13513.51
## [15] 13888.89 19230.77 13513.51 19230.77 15625.00 15151.52Las filas n1 es el número de conglomerados muestreados, m1 es el número de unidades muestreadas de cada conglomerado seleccionado, t1 son los totales estimados por expansión elemental y v1 son sus varianzas estimadas; y las dos últimas columnas son la media y las varianzas de las filas.
Este código muestra que el estimador de expansión elemental es insesgado y homogéneo.
La varianza de la etapa elemental es más exacta cuando los conglomerados tienen medias similares. Aquí no es necesario tomar la varianza de las dos etapas. Tambien, importa poco la distribución de las 600 unidades entre las dos etapas, esto es, \(600=n.m\).
El hecho de tener medias similares en los conglomerados reduce la varianza del estimador del total por expansión elemental a una sola etapa y su varianza es calculada con la varianza elemental v1x.