Find $E[|\sum X_i \sum Y_j|]$ where $X_i,Y_j \sim Exp(\lambda)$ and iid.
Is this the same thing as Finding $E[\sum X_i \sum Y_j]$?
Is $$E[|\sum X_i \sum Y_j|]= \sum E[X_i] \sum E[Y_j]?$$
2026-03-27 07:20:00.1774596000
Is $E[|\sum X_i \sum Y_j|]= \sum E[X_i] \sum E[Y_j]?$ where $X_i,Y_j \sim Exp(\lambda)$ and iid.
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Yes. Recall $|a|=a$ if $a>0$. Since $P(X_i>0)=P(Y_i>0)=1$, all the sums in your problem are non-negative, with probability 1, and the absolute value signs might as well not be there.