Variables

Procesamiento de los datos

  data <- read.csv("hour.csv", na.strings=FALSE, strip.white=TRUE)

  spring <- data %>% filter(season==1)
  summer <- data %>% filter(season==2)
  fall   <- data %>% filter(season==3)
  winter <- data %>% filter(season==4)
  
  dSpring <- kde2d(x = spring$temp, y = spring$hum, n = 100)
  dSummer <- kde2d(x = summer$temp, y = summer$hum, n = 100)
  dFall   <- kde2d(x = fall$temp,   y = fall$hum,   n = 100)
  dWinter <- kde2d(x = winter$temp, y = winter$hum, n = 100)

  #listas
  dSpring$z <- dSpring$z/sum(dSpring$z)
  dSummer$z <- dSummer$z/sum(dSummer$z)
  dFall$z   <- dFall$z/sum(dFall$z)
  dWinter$z <- dWinter$z/sum(dWinter$z)

  #densidades
  cSpring <- kde2d(x = spring$cnt, y = spring$temp, n = 100)
  cSummer <- kde2d(x = summer$cnt, y = summer$temp, n = 100)
  cFall   <- kde2d(x = fall$cnt,   y = fall$temp,   n = 100)
  cWinter <- kde2d(x = winter$cnt, y = winter$temp, n = 100)
  cSpring$z <- cSpring$z/sum(cSpring$z)
  cSummer$z <- cSummer$z/sum(cSummer$z)
  cFall$z   <- cFall$z/sum(cFall$z)
  cWinter$z <- cWinter$z/sum(cWinter$z)
  
  
  r1<-sum(dSpring$z[dSpring$x < 0.7,dSpring$y > 0.59 & dSpring$y < 0.61])  
  r2<-sum(dSummer$z[dSummer$x < 0.7,dSummer$y > 0.59 & dSummer$y < 0.61])
  r3<-sum(dFall$z[dFall$x < 0.7,dFall$y > 0.59 & dFall$y < 0.61])
  r4<-sum(dWinter$z[dWinter$x < 0.7,dWinter$y > 0.59 & dWinter$y < 0.61])
  r5<-sum(cSummer$z[cSummer$x > 142,cSummer$y > 0.59 & cSummer$y < 0.61])
  r6<-sum(cWinter$z[cWinter$x > 142,cWinter$y > 0.59 & cWinter$y < 0.61])
  temp<-matrix(rep(dSpring$x,100),nrow=100)
  hum <-matrix(rep(dSpring$y,100),nrow=100,byrow=TRUE)
  springE_x1<-sum(temp*dSpring$z)
  springE_x2<-sum(hum*dSpring$z)
  springV_x1<-sum((temp*temp)*dSpring$z) - sum((temp*dSpring$z)*(temp*dSpring$z))
  springV_x2<-sum((hum*hum)*dSpring$z) - sum((hum*dSpring$z)*(hum*dSpring$z))
  r7_spring<-c(springE_x1,springE_x2,springV_x1,springV_x2)
  temp<-matrix(rep(dSummer$x,100),nrow=100)
  hum <-matrix(rep(dSummer$y,100),nrow=100,byrow=TRUE)
  summerE_x1<-sum(temp*dSummer$z)
  summerE_x2<-sum(hum*dSummer$z)
  summerV_x1<-sum((temp*temp)*dSummer$z) - sum((temp*dSummer$z)*(temp*dSummer$z))
  summerV_x2<-sum((hum*hum)*dSummer$z) - sum((hum*dSummer$z)*(hum*dSummer$z))
  r7_summer<-c(summerE_x1,summerE_x2,summerV_x1,summerV_x2)
  temp<-matrix(rep(dFall$x,100),nrow=100)
  hum <-matrix(rep(dFall$y,100),nrow=100,byrow=TRUE)
  fallE_x1<-sum(temp*dFall$z)
  fallE_x2<-sum(hum*dFall$z)
  fallV_x1<-sum((temp*temp)*dFall$z) - sum((temp*dFall$z)*(temp*dFall$z))
  fallV_x2<-sum((hum*hum)*dFall$z) - sum((hum*dFall$z)*(hum*dFall$z))
  r7_fall<-c(fallE_x1,fallE_x2,fallV_x1,fallV_x2)
  temp<-matrix(rep(dWinter$x,100),nrow=100)
  hum <-matrix(rep(dWinter$y,100),nrow=100,byrow=TRUE)
  winterE_x1<-sum(temp*dWinter$z)
  winterE_x2<-sum(hum*dWinter$z)
  winterV_x1<-sum((temp*temp)*dWinter$z) - sum((temp*dWinter$z)*(temp*dWinter$z))
  winterV_x2<-sum((hum*hum)*dWinter$z) - sum((hum*dWinter$z)*(hum*dWinter$z))
  r7_winter<-c(winterE_x1,winterE_x2,winterV_x1,winterV_x2)
  temp <- matrix(rep(cSpring$y,100),nrow=100,byrow=TRUE) 
  cnt <- matrix(rep(cSpring$x,100),nrow=100) 
  springE_x1<-sum(temp*cSpring$z)
  springE_x3<-sum(cnt*cSpring$z)
  springV_x1<-sum((temp*temp)*cSpring$z) - sum((temp*cSpring$z)*(temp*cSpring$z))
  springV_x3<-sum((cnt*cnt)*cSpring$z) - sum((cnt*cSpring$z)*(cnt*cSpring$z))
  r8_spring<-c(springE_x1,springE_x3,springV_x1,springV_x3)
  temp <- matrix(rep(cSummer$y,100),nrow=100,byrow=TRUE) 
  cnt <- matrix(rep(cSummer$x,100),nrow=100) 
  summerE_x1<-sum(temp*cSummer$z)
  summerE_x3<-sum(cnt*cSummer$z)
  summerV_x1<-sum((temp*temp)*cSummer$z) - sum((temp*cSummer$z)*(temp*cSummer$z))
  summerV_x3<-sum((cnt*cnt)*cSummer$z) - sum((cnt*cSummer$z)*(cnt*cSummer$z))
  r8_summer<-c(summerE_x1,summerE_x3,summerV_x1,summerV_x3)
  temp <- matrix(rep(cFall$y,100),nrow=100,byrow=TRUE) 
  cnt <- matrix(rep(cFall$x,100),nrow=100) 
  fallE_x1<-sum(temp*cFall$z)
  fallE_x3<-sum(cnt*cFall$z)
  fallV_x1<-sum((temp*temp)*cFall$z) - sum((temp*cFall$z)*(temp*cFall$z))
  fallV_x3<-sum((cnt*cnt)*cFall$z) - sum((cnt*cFall$z)*(cnt*cFall$z))
  r8_fall<-c(fallE_x1,fallE_x3,fallV_x1,fallV_x3)
  temp <- matrix(rep(cWinter$y,100),nrow=100,byrow=TRUE) 
  cnt <- matrix(rep(cWinter$x,100),nrow=100) 
  winterE_x1<-sum(temp*cWinter$z)
  winterE_x3<-sum(cnt*cWinter$z)
  winterV_x1<-sum((temp*temp)*cWinter$z) - sum((temp*cWinter$z)*(temp*cWinter$z))
  winterV_x3<-sum((cnt*cnt)*cWinter$z) - sum((cnt*cWinter$z)*(cnt*cWinter$z))
  r8_winter<-c(winterE_x1,winterE_x3,winterV_x1,winterV_x3)
  r9_spring<-cov(dSpring$x, dSpring$y)
  r9_summer<-cov(dSummer$x, dSummer$y)
  r9_fall<-cov(dFall$x,   dFall$y  )
  r9_winter<-cov(dWinter$x, dWinter$y)
  r9<-c(r9_spring,r9_summer,r9_fall,r9_winter)
  r10_spring<-cov(cSpring$x, cSpring$y)
  r10_summer<-cov(cSummer$x, cSummer$y)
  r10_fall<-cov(cFall$x,   cFall$y  )
  r10_winter<-cov(cWinter$x, cWinter$y)
  r10<-c(r10_spring,r10_summer,r10_fall,r10_winter)

1. \(P(x_1<0.7 \mid x_2=0.6 \cap s_1 )\)

  r1
## [1] 0.03278237

2. \(P(x_1<0.7 \mid x_2=0.6 \cap s_2 )\)

  r2
## [1] 0.02978353

3. \(P(x_1<0.7 \mid x_2=0.6 \cap s_3 )\)

  r3
## [1] 0.01524592

4. \(P(x_1<0.7 \mid x_2=0.6 \cap s_4 )\)

  r4
## [1] 0.04409967

5. \(P(x_3>142 \mid x_1 =0.6 \cap s_2)\)

  r5
## [1] 0.04484594

6. \(P(x_3>142 \mid x_1 =0.6 \cap s_4)\)

  r6
## [1] 0.02779899

7. Si \(f(x_1,x_2)\) para cada \(s_i\) calcule, * \(E[x_1]\) * \(E[x_2]\) * \(V[x_1]\) * \(V[x_2]\)

Spring

  r7_spring
## [1] 0.2991682 0.5791163 0.1037561 0.3743206

Summer

  r7_summer
## [1] 0.5459477 0.6235850 0.3179421 0.4305863

Fall

  r7_fall
## [1] 0.7067466 0.6321321 0.5083733 0.4317608

Winter

  r7_winter
## [1] 0.4224813 0.6629364 0.1938805 0.4710746

8. Si \(f(x_1,x_3)\) para cada \(s_i\) calcule, * \(E[x_1]\) * \(E[x_3]\) * \(V[x_1]\) * \(V[x_3]\)

Spring

  r8_spring
## [1] 3.033282e-01 1.215682e+02 1.062909e-01 2.894148e+04

Summer

  r8_summer
## [1] 5.512044e-01 2.283579e+02 3.234436e-01 8.688719e+04

Fall

  r8_fall
## [1] 7.110093e-01 2.546409e+02 5.144196e-01 1.026506e+05

Winter

  r8_winter
## [1] 4.271750e-01 2.172567e+02 1.976867e-01 7.989071e+04

9. Calcule \(Cov(x_1,x_2)\)

  r9
## [1] 0.06011291 0.05626569 0.04472401 0.04472401

10. Calcule \(Cov(x_1,x_3)\)

  r10
## [1] 48.09033 64.03571 51.96504 51.43261