Question

An experiment is to flip a coin until a head appears for the first time. Assume the coin may be biased, i.e., assume that the probability the coin turns up heads on a flip is a constant p (0 < p < 1). Let X be the random variable that counts the number of flips needed to see the first head.

(a) Let k ≥ 1 be an integer. Compute the probability mass function (pmf) p(k) = P(X = k).

(b) If p = 1/3 compute P(2 ≤ X < 4) and P(1 < X < 3).

(c) If p = 1/3 compute P(X > 2).

(d) If p = 1/2 compute P(X is even).

Answer 1