3. If X has density function f, show that E[g(X)] = - g(x) f(x) dx...
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3. If X has density function
f, show that E[g(X)] = ∫-∞∞ g(x) f(x) dx HINT: Using Theoretical Exercise 2, start with E[g(X)] = ∫0∞ P(g(X) > y) dy - ∫0∞ P(g(X) < -y) dy and then proceed as in the proof given in the text when g(X) = 0.
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