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Consider 3 trials each having the same probability of success

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.

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.

(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.

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.

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