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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