Let $\displaystyle X,Y$ be two discrete random variables having finite moments (I assume this means $\displaystyle E(X)<\infty$). Show that

a)if $\displaystyle X\geq 0$, then $\displaystyle E(X)\geq 0$

b)if $\displaystyle X\leq Y$, then $\displaystyle E(X)\leq E(Y)$

HINT: You may consider the variable $\displaystyle Y-X$.

Again, with so much to do in so little time, I need help.