Example 7.15

01/30/13

x <- 0:10
x

##  [1]  0  1  2  3  4  5  6  7  8  9 10

freq <- c(29, 71, 82, 89, 65, 45, 24, 7, 4, 1, 3)  # x is observations
prop <- freq/sum(freq)

xbar <- sum(x * prop)
xbar

## [1] 2.979

x2bar <- sum(x^2 * prop)
x2bar

## [1] 12.4

Plug in formula for \( \hat{p} \) and \( \hat{r} \).

phat <- xbar/(x2bar - xbar^2)
phat

## [1] 0.8437

rhat <- xbar^2/(x2bar - xbar^2 - xbar)
rhat

## [1] 16.07