Question

For $n \in \mathbb{N}$, let $Z_n$ be the smallest order statistic based on a random sample of size $n$ from the $U(0,1)$ distribution. Let $nZ_n \xrightarrow{d} Z$ as $n \to \infty$ for some random variable $Z$. Then $P(Z \leq \ln 3)$ is equal to:

• A. $\frac{1}{4}$
• B. $\frac{2}{3}$
• C. $\frac{3}{4}$
• D. $\frac{1}{3}$

Answer 1

Answer: (B)

$\frac{2}{3}$

Answer 2

The correct option is (B): $\frac{2}{3}$