# R-program for Supplementary Exercise 4.71 of IPS7e

x <- c(540+(0:4)*5)
px <- c(.1, .25, .3, .25, .1)
mean <- sum(x*px); mean
var <- sum((x-mean)^2*px); var
sd <- sqrt(var); sd

# same thing for xF = temperature in F
xF <- 32 + 1.8*x
meanF <- sum(xF*px); meanF
varF <- sum((xF-meanF)^2*px); varF
sdF <- sqrt(varF); sdF