Let $X_1, X_2, \dots$ be i.i.d. continuous random variables and $N$ be a random variable supported on $\{0, 1, 2, \dots\}$ and independent on the $X_i$ .
How can I compute $Var\left[\left(\sum_{j=1}^N X_j\right)^2\right]$ ?
2026-03-31 14:26:07.1774967167
Variance of squared random sum of random variables
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