Replicating Arbitrary Payoffs with Calls and Puts

You are given the following three quantities for a random variable $X$: - $E[X]$ - $E[\max(0, X)]$ - $E[\min(0, X)]$ Let $f$ be a twice continuously differentiable function. 1. Write a formula expressing $E[f(X)]$ in terms of $f$, its derivatives, and expectations of call/put-type payoffs on $X$. 2. Interpret each term financially. What roles do stocks, bonds, calls, and puts play in the representation? 3. How do the given quantities $E[X]$, $E[\max(0,X)]$, and $E[\min(0,X)]$ map onto standard financial instruments?