Let X 1 , X 2 , ... be independent and identically distributed (i.i.d.) random variables having a χ 2 -distribution with 5 degrees of freedom. Let a &in; &reals; be a constant. Then the limiting distribution of a × X 1 + ... + X n - 5n √n is a:

Question

Mathematics · Probability and Statistics

Let X 1 , X 2 , ... be independent and identically distributed (i.i.d.) random variables having a χ 2 -distribution with 5 degrees of freedom. Let a &in; &reals; be a constant. Then the limiting distribution of a × X 1 + ... + X n - 5n √n is a:

Verified Solution4 OptionsUpdated: October 2026👁️1 View

Share:

Correct answer

Standard normal distribution for an appropriate value of a

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

Preparing for Mathematics?

Practice full-length mock tests with real exam timers, instant score analysis, and all-India ranking.

Start Free Mock Test →

Chapter Practice

Want more practice questions on Probability and Statistics?

Solve complete topic-wise tests with detailed solutions on GkGet.

Practice Probability and Statistics MCQs →

Recommended practice questions in Mathematics · Probability and Statistics

Browse More Mathematics →

1

Mahatma Gandhi's last fast unto death in 1948 was primarily against which of the following?

Solve Question→

2

What was the primary meaning of 'Swaraj' as popularized by Mahatma Gandhi during India's independence movement?

Solve Question→

3

What was one major impact of India’s independence on its economy?

Answer 1

Degenerate distribution for an appropriate value of a

Answer 2

Standard normal distribution for an appropriate value of a

Answer 3

χ 2 -distribution for an appropriate value of a

Answer 4

Gamma distribution for an appropriate value of a

Let X 1 , X 2 , ... be independent and identically distributed (i.i.d.) random variables having a χ 2 -distribution with 5 degrees of freedom. Let a &in; &reals; be a constant. Then the limiting distribution of a × X 1 + ... + X n - 5n √n is a:

Download Single Question PDF

Share with Friends & Study Groups

Preparing for Mathematics?

Practice by Subject

Practice by Exam

Topic-Wise Solved Questions

Let X 1 , X 2 , ... be independent and identically distributed (i.i.d.) random variables having a &chi; 2 -distribution with 5 degrees of freedom. Let a &in; &reals; be a constant. Then the limiting distribution of a &times; X 1 + ... + X n - 5n &radic;n is a:

Download Single Question PDF

Share with Friends & Study Groups

Preparing for Mathematics?

Related Practice Questions

Practice by Subject

Practice by Exam

Topic-Wise Solved Questions

Let X 1 , X 2 , ... be independent and identically distributed (i.i.d.) random variables having a χ 2 -distribution with 5 degrees of freedom. Let a &in; &reals; be a constant. Then the limiting distribution of a × X 1 + ... + X n - 5n √n is a: