4.55. The standard deviation of a discrete probability distribution is

" = VSCv - m) P{y)-

(a) Suppose y = 1 with probability 0.50 and y = 0 with probability 0.50, such as in Example 4.8

(page 91). Show that a = 0.50.

(b) Suppose y = 1 with probability tt and y = 0 with probability 1 - tt, where tt represents a number between 0 and 1. Show that p. - tt and that a = ^(l — tt).

(c) Show that the standard error of a sample proportion for a random sample of size n equals

^7T(1 - TT)/n.