Mathematics · Estimation Theory
Consider a population distributed according to f θ (x), which depends on an unknown parameter θ. Let X̄ denote the sample mean of a random sample X 1 , ..., X n . For which of the following cases is X̄ the Minimum Variance Unbiased Estimator (MVUE) of θ? I. f θ (x) ∝ exp{-θx} for x ≥ 0; θ > 0 II. f θ (x) ∝ exp{-(θ - x) 2 } for -∞ θ (x) ∝ θ x /x! for x = 0, 1, 2, ...; θ > 0 IV. f θ (x) ∝ θ x for x = 0, 1, 2, ...; 0 < θ < 1
Verified Solution4 OptionsUpdated: October 2026👁️1 View
Share:
- 1Only I and III
- 2Only II and III✓
- 3Only I and IV
- 4Only II and IV
Correct answer
Only II and III
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 Estimation Theory MCQs →Want more practice questions on Estimation Theory?
Solve complete topic-wise tests with detailed solutions on GkGet.
Related Practice Questions
Recommended practice questions in Mathematics · Estimation Theory