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:
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:
Updated On: Oct 1, 2024
- \( \frac{1}{4} \)
- \( \frac{2}{3} \)
- \( \frac{3}{4} \)
- \( \frac{1}{3} \)
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The Correct Option is B
Solution and Explanation
The correct option is (B): \( \frac{2}{3} \)
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