Mathematics · Statistics
Let X1, X2, ..., Xn (n ≥ 3) be a random sample from a population with an absolutely continuous cumulative distribution function F(·). The corresponding order statistics are X1:n < X2:n < ... < Xn:n. For r = 2, 3, define Yr,n = nF(Xr:n). Suppose that Yr,n converges in distribution to a random variable Yr as n → ∞, for r = 2, 3. Then, which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
Share:
- 1Y2 follows a gamma distribution with E(Y2) = 2✓
- 2E(Y3,n) → 3 as n → ∞
- 3Y3 follows a beta distribution with E(Y3) = 1/3
- 4Y2,n follows a beta distribution with parameters 2 and n - 1
Correct answer
Y2 follows a gamma distribution with E(Y2) = 2
Download Single Question PDF
Save this question and verified answer as a clean study sheet with live clickable link.
👥
Share with Friends & Study Groups
Challenge your peer aspirants on WhatsApp or Telegram to solve this question!
Online Test Series
Start Free Mock Test →Preparing for Mathematics?
Practice full-length mock tests with real exam timers, instant score analysis, and all-India ranking.
Chapter Practice
Practice Statistics MCQs →Want more practice questions on Statistics?
Solve complete topic-wise tests with detailed solutions on GkGet.
Related Practice Questions
Recommended practice questions in Mathematics · Statistics