Probability distribution, expected value.

(3) Suppose that a biased coin has probability of heads equal to p. Find the expectation of the number of heads minus the number of tails for n inde- pendent flips. (4) Consider the sample space S = {1, 2, 3, . . . 100}. Let X(n) = n. (a) Compute E(X) for the uniform distribution. (b) Compute E(X) for the probability distribution 1 P(n) = 150 if n even 2 150 if n odd (5) Let S = {1, 2, 3,...} with the probability distribution P(n) = 1 n(n + 1) Find the expectation of X(n) = 10 if it's defined