Mathematics · Probability Theory
Let {Xn, Yn : n ≥ 1} and (X, Y) be random variables on a probability space (Ω, F, P). Which of the following implications is correct?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
Share:
- 1Convergence in distribution always implies convergence almost surely
- 2If Xn → X in probability and Yn → Y in probability, then Xn + Yn → X + Y in distribution✓
- 3If Xn → X in distribution and Yn → 0 in distribution, then XnYn → X in distribution
- 4If Xn → X in distribution and Yn → Y in distribution, then Xn + Yn → X + Y in distribution
Correct answer
If Xn → X in probability and Yn → Y in probability, then Xn + Yn → X + Y in distribution
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 Probability Theory MCQs →Want more practice questions on Probability Theory?
Solve complete topic-wise tests with detailed solutions on GkGet.
Related Practice Questions
Recommended practice questions in Mathematics · Probability Theory