Let X ∼ Binomial(5, p), and let Y ∼ Geometric(p). You run two independent sets of Bernoulli trials to make one observation from X and one from Y. Suppose you observe X = 1 and Y = 4.

Use S to denote a success in any trial, and F to denote a failure.

Say whether each of the following statements is correct.

a. Both sets of trials had four failures and one success.

b. For Y, the trials must have been in the order FFFFS, but for X they could have occurred in any order.

c. P(X = 1) = 5p(1 − p)

4

, whereas P(Y = 4) = p(1 − p)

4

.

d. P(X = 1) = P(Y = 4) = p(1 − p)

4

.