Question
Prove that for a hypergeometric random variable $X$ with parameters $n, N$, and $r$,$$E[X]=\frac{n r}{N}$$and$$\operatorname{Var}[X]=\frac{n r(N-r)(N-n)}{N^2(N-1)}$$
Step 1
A hypergeometric random variable $X$ models the number of successes in a sample of size $n$ drawn without replacement from a finite population of size $N$ containing exactly $r$ successes. The probability mass function of $X$ is given by: $$ P(X = k) = Show more…
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