55. * The variance of a discrete probability distribution is 0 =0- P(3)

a) Suppose Y = I with probability .5 and Y=0 with probability 5, such as in Example 4.7 on preference for Democratic and Republican candidates Using each formula show that o25. and hence the standard deviation = .50.

b) Suppose 1 with probability and Y=0 with probability 1-7. where xr denotes a fixed number between 0 and 1. Show that = and that o=(-)

c) Refer to

(b) Show that the standard error of a sample proportion for a random sample of size n equals(1). (Hint: Recall that a proportion equals a mean for a vanable taking values 0 and ] )