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suppose that airplanes arrive at an airport according to a Poisson process a rate of 3 per minute
2026-04-17 22:37:10.1776465430
if $X$ = number of planes that arrive in an hour, what is $E[X(1-X)]$
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Regardless of your specific problem, notice that:
$\mathbb{E}[X(1-X)]=\mathbb{E}[X-X^2]= \mathbb{E}[X]-\mathbb{E}[X^2]$
And that $\mathbb{E}[X^2]=Var(X)-\big( \mathbb{E}[X] \big)^2$. And for most known distributions it is a simple matter of looking what the variance and the expectation are.