Let X have the binomial distribution with parameters n and p. Let Y have the binomial distribution with parameters n and p/k with k > 1. Let Z = kY.
a. Show that X and Z have the same mean.
b. Find the variances of X and Z. Show that, if p is small, then the variance of Z is approximately k times as large as the variance of X.
c. Show why the results above explain the higher variability in the bar heights in Fig. 6.2 compared to Fig. 6.1.