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.