# Thread: two easy questions I can't figure out

1. ## two easy questions I can't figure out

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

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

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.

2. Try markov or if you rather call it chebyshev's $\ne$.

For all $\epsilon>0$

$P(|X|>\epsilon)\le {E|X|\over\epsilon}=0$.

Same idea with the second, just use the second moment and write X-2 for my X.