# To illustrate the proof of Theorem 1, consider the

**Chapter 4, Problem 1**

(choose chapter or problem)

To illustrate the proof of Theorem 1, consider the randomvariable 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) E[g(X)] =.4i=1gi P[g(X) = gi], and show thatit equals!xg(x) f (x)

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