Let X1 and X2 be two i.i.d. p × 1 multivariate normal random vectors with mean μ and positive definite dispersion matrix ∑. Then which of the following random variables always has a central chi-square distribution 

This question was previously asked in
CSIR-UGC (NET) Mathematical Science: Held on (26 Nov 2020)
View all CSIR NET Papers >
  1. \(\frac{1}{2}\)(X1 - X2)T (X1 - X2)
  2. 2(X1 - X2)T (X1 - X2)
  3. 2(X1 - X2)T ∑-1(X1 - X2)
  4. \(\frac{1}{2}\)(X1 - X2)T ∑-1(X1 - X2)​

Answer (Detailed Solution Below)

Option 4 : \(\frac{1}{2}\)(X1 - X2)T ∑-1(X1 - X2)​
Free
Seating Arrangement
3.8 K Users
10 Questions 20 Marks 15 Mins

Detailed Solution

Download Solution PDF

\(\frac12\)(X1 - X2)T ∑-1(X1 - X2)​ has a central chi-square distribution 

Option (4) is correct

Latest CSIR NET Updates

Last updated on Jul 8, 2025

-> The CSIR NET June 2025 Exam Schedule has been released on its official website.The exam will be held on 28th July 2025.

-> The CSIR UGC NET is conducted in five subjects -Chemical Sciences, Earth Sciences, Life Sciences, Mathematical Sciences, and Physical Sciences. 

-> Postgraduates in the relevant streams can apply for this exam.

-> Candidates must download and practice questions from the CSIR NET Previous year papers. Attempting the CSIR NET mock tests are also very helpful in preparation.

Get Free Access Now
Hot Links: teen patti wala game teen patti joy apk teen patti master official