申論題

1.(20%) For a random variable x defined on the real number line, denote its probability density function and cumulative distribution function as f(x) and Fx(a), respectively. By definition,
and the expectation of any function g(x) can be derived as

(b) (10%) Prove that H_x(η) -(η-E[x]) = E(x-η)⁺],where (x-η)⁺=