Prove that the expectation is a linear system. Ex~p(x)[a (X) + b g(X)] = a E...

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Prove that the expectation is a linear system. Ex~p(x)[a ƒ(X) + b g(X)] = a E Ex~P(x)[ƒ(X)] + b Ex~p(x)[9(X)] You may treat X as a discrete variable. Hint: Use the identity Ex~P(x) [f(x)] = [P(X)ƒ (X) X Prove that the expectation is a linear system. Ex~p(x)[a ƒ(X) + b g(X)] = a E Ex~P(x)[ƒ(X)] + b Ex~p(x)[9(X)] You may treat X as a discrete variable. Hint: Use the identity Ex~P(x) [f(x)] = [P(X)ƒ (X) X