10. Consider 3 trials, each having the same probability of success. Let X denote the total number of successes in these trials. If E[X] = 1.8, what is

(a) the largest possible value of P(X = 3);

(b) the smallest possible value of P(X = 3)?

In both cases construct a probability scenario that results in P(X = 3) having the stated value.

HINT: For part

(b) you might start by letting U be a uniform random variable on (0, 1) and then defining the trials in terms of the value of U.