Laboratorio 2

El siguiente laboratorio encuentra ciertas probabilidades, utiliza el DataSet de la demanda de bicicletas en EEUU.

data <- read.csv("hour.csv",na.strings = FALSE,strip.white = TRUE)
data <- dplyr::select(data,season,temp,hum,cnt)

Crear las matrices para cada una de las estaciones

spring <- filter(data,season==1)
s1 <- kde2d(x=spring$temp,y=spring$hum,n=100)
s1$z <-s1$z/sum(s1$z)
s1_ <- kde2d(x=spring$temp,y=spring$cnt,n=100)
s1_$z <- s1_$z/sum(s1_$z)
rm(spring)
summer <- filter(data,season==2)
s2 <- kde2d(x=summer$temp,y=summer$hum,n=100)
s2$z <- s2$z/sum(s2$z)
s2_ <- kde2d(x=summer$temp,y=summer$cnt,n=100)
s2_$z <- s2_$z/sum(s2_$z)
rm(summer)
fall <- filter(data,season==3)
s3 <- kde2d(x=fall$temp,y=fall$hum,n=100)
s3$z <- s3$z/sum(s3$z)
s3_ <- kde2d(x=fall$temp,y=fall$cnt,n=100)
s3_$z <- s3_$z/sum(s3_$z)
rm(fall)
winter <- filter(data,season==4)
s4 <- kde2d(x=winter$temp,y=winter$hum,n=100)
s4$z <- s4$z/sum(s4$z)
s4_ <- kde2d(x=winter$temp,y=winter$cnt,n=100)
s4_$z <- s4_$z/sum(s4_$z)
rm(winter)

Entregables

1. P(x1>0.7 | x2 = 0.6 & s1)

b <- (s1$y >= 0.6 & s1$y <= 0.7)
a <- s1$x > 0.7
sum(s1$z[a,b])

[1] 2.913279e-07

R// P(x1>0.7 | x2 = 0.6 & s1) = 2.913279e-07

2. P(x1>0.7 | x2 = 0.6 & s2)

b <- (s2$y >= 0.6 & s2$y <= 0.7)
a <- s2$x > 0.7
sum(s2$z[a,b])

[1] 0.02302887

R// P(x1>0.7 | x2 = 0.6 & s2) = 0.02302887

3. P(x1>0.7 | x2 = 0.6 & s3)

b <- (s3$y >= 0.6 & s3$y <= 0.7)
a <- s3$x > 0.7
sum(s3$z[a,b])

[1] 0.09653756

R// P(x1>0.7 | x2 = 0.6 & s3) = 0.09653756

4. P(x1>0.7 | x2 = 0.6 & s4)

b <- (s4$y >= 0.6 & s4$y <= 0.7)
a <- s4$x > 0.7
sum(s4$z[a,b])

[1] 0.001974558

R// P(x1>0.7 | x2 = 0.6 & s4) = 0.001974558

5. P(x3>0.7 | x1 = 0.6 & s2)

a <- (s2_$y >142)
b <- (s2_$x >= 0.6 & s2_$x <= 0.7)
sum(s2_$z[a,b])

[1] 0.05132424

R// P(x3>0.7 | x1 = 0.6 & s2) = 0.05132424

6. P(x3>0.7 | x1 = 0.6 & s4)

a <- (s4_$y >142)
b <- (s4_$x >= 0.6 & s4_$x <= 0.7)
sum(s4_$z[a,b])

[1] 0.01547928

R// P(x3>0.7 | x1 = 0.6 & s4) = 0.01547928

7. Si f(x1,x2) calcular los siguientes incisos para cada si

a)E(x1)

Es1<-sum(s1$x*s1$z)
Es2<-sum(s2$x*s2$z)
Es3<-sum(s3$x*s3$z)
Es4<-sum(s4$x*s4$z)
Es1

[1] 0.2991682

Es2

[1] 0.5459477

Es3

[1] 0.7067466

Es4

[1] 0.4224813

R// E(x1) para s1 = 0.2991682 E(x1) para s2 = 0.5459477 E(x1) para s3 = 0.7067466 E(x1) para s4 = 0.4224813

2. E(x2)

Es1<-sum(s1$y*s1$z)
Es2<-sum(s2$y*s2$z)
Es3<-sum(s3$y*s3$z)
Es4<-sum(s4$y*s4$z)
Es1

[1] 0.3988117

Es2

[1] 0.575636

Es3

[1] 0.602689

Es4

[1] 0.5427166

R// E(x2) para s1 = 0.3988117 E(x2) para s2 = 0.575636 E(x2) para s3 = 0.602689 E(x2) para s4 = 0.5427166

3. V(x1)

Vs1 <- (sum((s1$x*s1$x)*s1$z))-(sum((s1$x*s1$z)*(s1$x*s1$z)))
Vs2 <- (sum((s2$x*s2$x)*s2$z))-(sum((s2$x*s2$z)*(s2$x*s2$z)))
Vs3 <- (sum((s3$x*s3$x)*s3$z))-(sum((s3$x*s3$z)*(s3$x*s3$z)))
Vs4 <- (sum((s4$x*s4$x)*s4$z))-(sum((s4$x*s4$z)*(s4$x*s4$z)))
Vs1

[1] 0.1037561

Vs2

[1] 0.3179421

Vs3

[1] 0.5083733

Vs4

[1] 0.1938805

R// V(x1) para s1 = 0.1037561 V(x1) para s2 = 0.3179421 V(x1) para s3 = 0.5083733 V(x1) para s4 = 0.1938805

4. V(x2)

Vs1 <- (sum((s1$y*s1$y)*s1$z))-(sum((s1$y*s1$z)*(s1$y*s1$z)))
Vs2 <- (sum((s2$y*s2$y)*s2$z))-(sum((s2$y*s2$z)*(s2$y*s2$z)))
Vs3 <- (sum((s3$y*s3$y)*s3$z))-(sum((s3$y*s3$z)*(s3$y*s3$z)))
Vs4 <- (sum((s4$y*s4$y)*s4$z))-(sum((s4$y*s4$z)*(s4$y*s4$z)))
Vs1

[1] 0.1881472

Vs2

[1] 0.3544194

Vs3

[1] 0.3797295

Vs4

[1] 0.3227969

R// V(x2) para s1 = 0.1881472 V(x2) para s2 = 0.3544194 V(x2) para s3 = 0.3797295 V(x2) para s4 = 0.3227969

8. Si f(x1,x3) calcular los siguientes incisos para cada si

a)E(x1)

Es1<-sum(s1_$x*s1_$z)
Es2<-sum(s2_$x*s2_$z)
Es3<-sum(s3_$x*s3_$z)
Es4<-sum(s4_$x*s4_$z)
Es1

[1] 0.3033282

Es2

[1] 0.5512044

Es3

[1] 0.7110093

Es4

[1] 0.427175

R// E(x1) para s1 = 0.3033282 E(x1) para s2 = 0.5512044 E(x1) para s3 = 0.7110093 E(x1) para s4 = 0.427175

2. E(x2)

Es1<-sum(s1_$y*s1_$z)
Es2<-sum(s2_$y*s2_$z)
Es3<-sum(s3_$y*s3_$z)
Es4<-sum(s4_$y*s4_$z)
Es1

[1] 324.8036

Es2

[1] 480.4761

Es3

[1] 522.0728

Es4

[1] 448.4372

R// E(x2) para s1 = 324.8036 E(x2) para s2 = 480.4761 E(x2) para s3 = 522.0728 E(x2) para s4 = 448.4372

3. V(x1)

Vs1 <- (sum((s1_$x*s1_$x)*s1_$z))-(sum((s1_$x*s1_$z)*(s1_$x*s1_$z)))
Vs2 <- (sum((s2_$x*s2_$x)*s2_$z))-(sum((s2_$x*s2_$z)*(s2_$x*s2_$z)))
Vs3 <- (sum((s3_$x*s3_$x)*s3_$z))-(sum((s3_$x*s3_$z)*(s3_$x*s3_$z)))
Vs4 <- (sum((s4_$x*s4_$x)*s4_$z))-(sum((s4_$x*s4_$z)*(s4_$x*s4_$z)))
Vs1

[1] 0.1062909

Vs2

[1] 0.3234436

Vs3

[1] 0.5144196

Vs4

[1] 0.1976867

R// V(x1) para s1 = 0.1062909 V(x1) para s2 = 0.3234436 V(x1) para s3 = 0.5144196 V(x1) para s4 = 0.1976867

4. V(x2)

Vs1 <- (sum((s1_$y*s1_$y)*s1_$z))-(sum((s1_$y*s1_$z)*(s1_$y*s1_$z)))
Vs2 <- (sum((s2_$y*s2_$y)*s2_$z))-(sum((s2_$y*s2_$z)*(s2_$y*s2_$z)))
Vs3 <- (sum((s3_$y*s3_$y)*s3_$z))-(sum((s3_$y*s3_$z)*(s3_$y*s3_$z)))
Vs4 <- (sum((s4_$y*s4_$y)*s4_$z))-(sum((s4_$y*s4_$z)*(s4_$y*s4_$z)))
Vs1

[1] 124160.7

Vs2

[1] 260396.7

Vs3

[1] 294939.3

Vs4

[1] 238082.1

R// V(x2) para s1 = 124160.7 V(x2) para s2 = 260396.7 V(x2) para s3 = 294939.3 V(x2) para s4 = 238082.1