expectation of negative max function

Question

Im struggling with the following:

Define $Y$ = max(-(X+A), 0) where X and A are random variable, and $E$[X] > 0 and $E$[A] >= 0 How can I prove that $E$[Y] is always smaller or equal to 0?

Thanks in advance, James

Answer 1

You cannot.

Evidently we have $Y\geq0$ and consequently $\mathbb EY\geq0$.