An experiment consists of identical trials. Each trial can result in one of two possible outcomes: success or failure. The trials are inde- pendent. The probability of success is constant from trial to trial. Let X be a random variable that counts the number of trials necessary to obtain the first success. Note: Such an X is said to have geometric distribution. (a) Find a formula for P(X = x).
(b) Show that E(X) = 1/p.
(c) Give an example of a geometric experiment.