Let $\displaystyle X_{1},X_{2}...$ be iid random variables with mean $\displaystyle \mu$ and $\displaystyle E(X_{1}^{4})=1$. Set $\displaystyle \bar{X}_{n}=(X_{1}+...+X_{n})/n$. Show $\displaystyle \bar{X}_{n}\to\mu$ almost surely as $\displaystyle n\to \infty$.

So far all I have is convergence in probability from the weak law of large numbers. I don't see what the trick is to using the expected value.