Let $X_1,X_2,...$ be a sequence of independent random variables with $P(X_n = 3^n) = P(X_n = -3^n) = \frac{1}{2}$. Let $S_n = X_1 + ... + X_n$.
- Compute $E(X_n)$ for each $n$.
My guess for this one is that $E(X_n) = \frac{1}{2}\{\infty - \infty\}$ but that's only because $3^n$ would diverge to $\infty$ and $-3^n$ would diverge to $-\infty$. Is this assumption incorrect or could you tell what I may be missing?