# Question: To illustrate the proof of Theorem 4 1 consider the random

To illustrate the proof of Theorem 4.1, consider the random variable X, which takes on the values -2, -1, 0, 1, 2, and 3 with probabilities f (-2), f (-1), f (0), f (1), f (2), and f (3). If g(X) = X2, find

(a) g1, g2, g3, and g4, the four possible values of g(x);

(b) the probabilities P[g(X) = gi] for i = 1, 2, 3, 4;

(c)

And show that it equals

(a) g1, g2, g3, and g4, the four possible values of g(x);

(b) the probabilities P[g(X) = gi] for i = 1, 2, 3, 4;

(c)

And show that it equals

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