Question

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.