The problem is from A First Course in Stochastic Processes, second edition. Chapter 6, Problem 31.
The definition of M really confuses me. In this case, does it mean that n can go to infinity?
Here is what I started:
$f(x) = E\{E[[x+M-E(M)]^+| x + M - E(M)>0]\} = E\{E[x + M -E(M)| x+ M-E(M)>0]\}$
And then I stuck. I really appreciate it if someone can help me.