6.2 P5

A

\(E(X) = 62\)

60*(.1)+61*(.2)+62*(.4)+63*(.2)+64*(.1)
## [1] 62

\(V(F) = 1.2\)

x <- c(60,61,62,63,64)
p <- c(.1, .2, .4, .2, .1)
m <- 62
i <- 1
var <- 0

while(i <= length(x)){
  var <- var + p[i]*((x[i]-m)^2)
  i <- i + 1
}
var
## [1] 1.2

B

Theorem 6.2

\(E(X + c) = E(X)\)

\(E(T) = E(F-62) = E(F)-62\)

\(62 - 62 = 0\)

\(V(T) = V(F-62) = 1.2\)

x <- c(-2,-1,0,1,2)
p <- c(.1, .2, .4, .2, .1)
m <- 0
i <- 1
var <- 0

while(i <= length(x)){
  var <- var + p[i]*((x[i]-m)^2)
  i <- i + 1
}
var
## [1] 1.2

C

\(C = \frac{5}{9}(F-32)\)

\(E(C) = 16.67\)

x <- c(60,61,62,63,64)
ev <- 0
p <- c(.1, .2, .4, .2, .1)

#calculate celsius and put in a vector
celsius <- function(x){
  c <- (5/9)*(x-32)
  return(c)
}

#Find E(C)
i <- 1
while(i <= length(x)){
  ev <- ev + celsius(x[i])*p[i]
  i <- i + 1
}


ev
## [1] 16.66667

\(V(C) = 0.37\)

x <- c(60,61,62,63,64)
c <- c()
p <- c(.1, .2, .4, .2, .1)
m <- 16.67
i <- 1
var <- 0

#calculate celsius and put in a vector
celsius <- function(x){
  for(i in x){
    c <- c(c, (5/9)*(i-32))
  }
  return(c)
}

c <- celsius(x)

while(i <= length(x)){
  var <- var + p[i]*((c[i]-m)^2)
  i <- i + 1
}
var
## [1] 0.3703815