1. Let X be a random variable such that $\displaystyle E(|x|)=0$. Show that $\displaystyle P(X=0)=1$

2. Let X have mean 2 and variance 0. Show that $\displaystyle P(X=2)=1$.

They're both pretty simple and intuitively obvious, but with no other description of the random variable I really have no idea what properties to even work with.