Let $X_k$ be some indicator random variable such that $E(X_k) = p$. I'd like to calculate
$$E\left[\left(\frac{1}{n}\sum_{k=1}^n X_k\right)^2\right]$$
Is there an easy way to rewrite the sum and use the linearity of the expected value here? I thought about using something like the Multinomial Theorem, but I'm sure that there is an easier way to do this.