Question: (a)For X∼Pois(λ), Find E(5X).
Do we sum from 0 or 1?
2026-04-22 02:27:56.1776824876
Where to start summation from
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A Poisson random variable can be intuitively interpreted as the number of occurrences of something in a given interval, so it can take on $0$. A geometric random variable is intuitively the number of times before we get the first "success" in a sequence of Bernoulli trials, so it can also take on $0$ (think about that you get "success" at the first trial, so there is $0$ fails.). Hence the range of both types of random variables is $\{ 0, 1, \dots \}$.