Q37Section B (Section B)37 of 60

Shrinking urn asymptotics

A sample of size $n$ is drawn randomly (without replacement) from an urn containing $5n^{2}$ balls, of which $2n^{2}$ are red balls and $3n^{2}$ are black balls. Let $X_{n}$ denote the number of red balls in the selected sample. If $\ell=\lim_{n\to\infty}\dfrac{E(X_{n})}{n}$ and $m=\lim_{n\to\infty}\dfrac{\operatorname{Var}(X_{n})}{n}$ , then which of the following statements is/are TRUE?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Select every correct option, then submit.

Keyboard: A–D answer · S solution · ←/→ previous/next