Given that $x$ is a hypergeometric random variable with $N = 8 , n = 4$, and $r = 3$, compute the variance of $x$.
A) .732
B) .700
C) .469
D) .538

Question

Quizplus · Accepted Answer

The variance of a hypergeometric distribution is given by $\text{Var}(X) = n \cdot \frac{r}{N} \cdot \frac{N-r}{N} \cdot \frac{N-n}{N-1}$. Substituting the given values: $n = 4$, $r = 3$, $N = 8$, we get $\text{Var}(X) = 4 \cdot \frac{3}{8} \cdot \frac{5}{8} \cdot \frac{4}{7} = 0.5375$, which rounds to 0.538.

Given That xxx Is a Hypergeometric Random Variable With N=8,n=4N = 8 , n = 4N=8,n=4

Given That $x$ Is a Hypergeometric Random Variable With $N = 8 , n = 4$