6-11. Let the proportion of successes in a sample of size n be Y = X/n. Since Y = y and X = nY = ny are equivalent events (there exists a one-to-one correspondence between X and Y), it follows that P(Y = y) = P(X = ny).

Hence the distribution of Y can be determined from the (binomial) distribution of X. So for n = 5 trials of the random experiment in Exercise 6-10,

determine the probability distribution of Y. Then find E(Y) and V(Y) in terms of E(X) and V(X).