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
a=sample(0.5:5,1)
b=a/100
x1=rgamma(N1,a,b)
N2=1500
a=sample(0.5:5,1)
b=a/100
x2=rgamma(N2,a,b)
N3=2500
a=sample(0.5:5,1)
b=a/100
x3=rgamma(N3,a,b)
N4=3500
a=sample(0.5:5,1)
b=a/100
x4=rgamma(N4,a,b)
N5=5500
a=sample(0.5:5,1)
b=a/100
x5=rgamma(N5,a,b)
N6=4500
a=sample(0.5:5,1)
b=a/100
x6=rgamma(N6,a,b)
N7=6500
a=sample(0.5:5,1)
b=a/100
x7=rgamma(N7,a,b)
N8=7500
a=sample(0.5:5,1)
b=a/100
x8=rgamma(N8,a,b)
N9=8500
a=sample(0.5:5,1)
b=a/100
x9=rgamma(N9,a,b)
N10=9500
a=sample(0.5:5,1)
b=a/100
x10=rgamma(N10,a,b)
N11=10500
a=sample(0.5:5,1)
b=a/100
x11=rgamma(N11,a,b)
N12=11500
a=sample(0.5:5,1)
b=a/100
x12=rgamma(N12,a,b)
N13=12500
a=sample(0.5:5,1)
b=a/100
x13=rgamma(N13,a,b)
N14=13500
a=sample(0.5:5,1)
b=a/100
x14=rgamma(N14,a,b)
N15=14500
a=sample(0.5:5,1)
b=a/100
x15=rgamma(N15,a,b)
N16=15500
a=sample(0.5:5,1)
b=a/100
x16=rgamma(N16,a,b)
N17=16500
a=sample(0.5:5,1)
b=a/100
x17=rgamma(N17,a,b)
N18=17500
a=sample(0.5:5,1)
b=a/100
x18=rgamma(N18,a,b)
N19=18500
a=sample(0.5:5,1)
b=a/100
x19=rgamma(N19,a,b)
N20=19500
a=sample(0.5:5,1)
b=a/100
x20=rgamma(N20,a,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 4.000000e+00 5.000000e+00 6 1.000000e+01
## m1 200 1.500000e+02 1.200000e+02 100 6.000000e+01
## t1 21151974 1.937865e+07 2.021127e+07 20954167 2.042862e+07
## v1 783007281688 1.606742e+12 1.128590e+12 905251043931 1.183939e+12
## v1x 470602019517 6.728347e+11 5.597278e+11 503713802575 5.300960e+11
## [,6] [,7] [,8] [,9] [,10]
## n1 12 15 20 3 4.000000e+00
## m1 50 40 30 200 1.500000e+02
## t1 20869541 18830443 20074759 19562930 2.008362e+07
## v1 880082179056 867069522487 577318180102 619446783612 6.025058e+12
## v1x 499168957706 696997338704 577318180102 347871157081 3.017822e+11
## [,11] [,12] [,13] [,14] [,15]
## n1 5.000000e+00 6.000000e+00 1.000000e+01 12 15
## m1 1.200000e+02 1.000000e+02 6.000000e+01 50 40
## t1 1.984107e+07 1.953516e+07 2.019176e+07 19403081 19117979
## v1 3.522671e+12 2.485304e+12 1.039960e+12 745418705882 590125338300
## v1x 2.580322e+11 2.319507e+11 3.055784e+11 302259226008 388273623905
## [,16] [,17] [,18] [,19] [,20]
## n1 20 3.000000e+00 4.000000e+00 5.000000e+00 6
## m1 30 2.000000e+02 1.500000e+02 1.200000e+02 100
## t1 18685660 1.974123e+07 2.232197e+07 1.972889e+07 20153580
## v1 382328919686 1.032534e+12 1.928767e+12 1.324396e+12 995013488681
## v1x 382328919686 4.479614e+11 7.463543e+11 6.419837e+11 569267050310
## [,21] [,22] [,23] [,24] [,25]
## n1 10 12 15 20 3.000000e+00
## m1 60 50 40 30 2.000000e+02
## t1 19346669 19542703 20162317 19664263 1.983006e+07
## v1 793793376131 665230920873 778573246119 522992166557 1.082703e+13
## v1x 499659121493 446141293433 608230860372 522992166557 6.586497e+11
## [,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 2.110521e+07 2.095629e+07 2.061616e+07 1.942588e+07 2.040394e+07
## v1 6.306382e+12 3.778721e+12 2.585136e+12 1.992923e+12 1.479045e+12
## v1x 6.346426e+11 5.577566e+11 4.865628e+11 8.891264e+11 7.744795e+11
## [,31] [,32] [,33] [,34] [,35]
## n1 1.500000e+01 20 3.000000e+00 4.000000e+00 5.000000e+00
## m1 4.000000e+01 30 2.000000e+02 1.500000e+02 1.200000e+02
## t1 2.100652e+07 19869561 2.046009e+07 2.180255e+07 2.198815e+07
## v1 1.082973e+12 646529344772 2.924674e+12 2.674592e+12 2.228513e+12
## v1x 7.311053e+11 646529344772 2.929987e+11 4.930609e+11 4.225758e+11
## [,36] [,37] [,38] [,39] [,40]
## n1 6.000000e+00 10 12 15 20
## m1 1.000000e+02 60 50 40 30
## t1 2.013152e+07 19600554 19894015 19269706 19376945
## v1 1.643070e+12 856656639058 645777721584 596431892384 450820030925
## v1x 4.004300e+11 509101869830 449484576991 510822372528 450820030925
## [,41] [,42] [,43] [,44] [,45]
## 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 2.055172e+07 2.080335e+07 1.996455e+07 2.014410e+07 1.951290e+07
## v1 1.975391e+12 4.736419e+12 2.833988e+12 1.965600e+12 1.021359e+12
## v1x 5.497416e+11 5.500530e+11 4.791576e+11 4.145352e+11 4.879956e+11
## [,46] [,47] [,48] [,49] [,50]
## n1 12 15 20 3.000000e+00 4.000000e+00
## m1 50 40 30 2.000000e+02 1.500000e+02
## t1 19725576 20170705 20051822 2.132242e+07 1.837446e+07
## v1 947737835450 758506570972 463456439607 5.496395e+12 3.476638e+12
## v1x 504018895252 544693904701 463456439607 6.713955e+11 6.879074e+11
## [,51] [,52] [,53] [,54] [,55]
## n1 5.000000e+00 6.000000e+00 10 12 15
## m1 1.200000e+02 1.000000e+02 60 50 40
## t1 2.013011e+07 2.034697e+07 21072846 20151655 19623090
## v1 2.148670e+12 1.486267e+12 937587651204 679112240310 792117459466
## v1x 5.761798e+11 5.075060e+11 414642995566 372713064493 569892554427
## [,56] [,57] [,58] [,59] [,60]
## n1 20 3.000000e+00 4.000000e+00 5.000000e+00 6.000000e+00
## m1 30 2.000000e+02 1.500000e+02 1.200000e+02 1.000000e+02
## t1 19959713 1.933912e+07 2.193280e+07 2.006113e+07 2.092296e+07
## v1 481225469892 1.190586e+12 1.960659e+12 1.434217e+12 1.195970e+12
## v1x 481225469892 4.718844e+11 6.984163e+11 6.009744e+11 5.289828e+11
## [,61] [,62] [,63] [,64] [,65]
## n1 10 12 15 20 3.000000e+00
## m1 60 50 40 30 2.000000e+02
## t1 19530114 19882350 20088441 19375295 1.925548e+07
## v1 777530828439 644890103985 702996270675 534007732285 5.348898e+12
## v1x 592492961227 526943414964 627713562592 534007732285 4.626833e+11
## [,66] [,67] [,68] [,69] [,70]
## n1 4.000000e+00 5.000000e+00 6.000000e+00 10 12
## m1 1.500000e+02 1.200000e+02 1.000000e+02 60 50
## t1 1.917256e+07 1.926338e+07 2.010437e+07 18462423 19718986
## v1 3.559071e+12 2.226914e+12 1.562882e+12 979387627915 769060880529
## v1x 5.334343e+11 4.531517e+11 3.950633e+11 553747881073 485689179221
## [,71] [,72] [,73] [,74] [,75]
## n1 15 20 3.000000e+00 4.000000e+00 5.000000e+00
## m1 40 30 2.000000e+02 1.500000e+02 1.200000e+02
## t1 19710359 20105064 1.981742e+07 1.937573e+07 1.898775e+07
## v1 789131739285 465556355309 1.014018e+12 2.987752e+12 2.429111e+12
## v1x 527620734642 465556355309 4.041405e+11 4.309560e+11 3.983113e+11
## [,76] [,77] [,78] [,79] [,80]
## n1 6.000000e+00 10 12 15 20
## m1 1.000000e+02 60 50 40 30
## t1 1.928135e+07 20091858 20062391 22246350 19510143
## v1 1.623206e+12 873057735359 648424677085 670546264525 421697681692
## v1x 3.560236e+11 428732863242 389592261310 475464895722 421697681692
## [,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 1.931140e+07 2.085263e+07 1.921586e+07 2.002920e+07 2.065260e+07
## v1 4.514379e+12 4.340612e+12 2.753603e+12 2.136210e+12 1.119887e+12
## v1x 2.395568e+11 1.002119e+12 8.440103e+11 7.179159e+11 5.962923e+11
## [,86] [,87] [,88] [,89] [,90]
## n1 12 15 20 3.000000e+00 4.000000e+00
## m1 50 40 30 2.000000e+02 1.500000e+02
## t1 19919429 19478350 19031975 2.010985e+07 2.109820e+07
## v1 937963344920 739104980572 460174887446 1.480450e+12 1.294631e+12
## v1x 552300211038 533527397243 460174887446 4.840478e+11 5.400480e+11
## [,91] [,92] [,93] [,94] [,95]
## n1 5 6 10 12 15
## m1 120 100 60 50 40
## t1 20286343 20046197 19116087 20992846 20983306
## v1 926011392112 812373162874 768367028694 653239738223 664098773947
## v1x 459436046290 415369696344 522899305068 469018108576 525155071765
## [,96] [,97] [,98]
## n1 20 9.375000e+00 3.181579e+01
## m1 30 9.375000e+01 3.181579e+03
## t1 20546557 2.004786e+07 6.234759e+11
## v1 485310268978 1.679160e+12 2.643007e+24
## v1x 485310268978 5.135922e+11 1.758927e+22Las 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 las dos etapas. Tambien, importa poco la distribución de las 600 unidades entre las dos etapas, esto es, \(600=n.m\).