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Let X1, X2, X3 and X4 he independent and identically distributed Bernoulli \(\left(\frac{1}{3}\right)\) random variables. Let X(1), X(2), X(3) and X(4) denote the corresponding order statistics. Which of the following is true?

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CSIR UGC (NET) Mathematical Science: Held On (7 June 2023)
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  1. X(1) and X(4) are independent.
  2. Expectation of X2 is \(\frac{1}{2}\).
  3. Variance of X2 is \(\frac{8}{81}\).
  4. X(4) is a degenerate random variable.

Answer (Detailed Solution Below)

Option 3 : Variance of X2 is \(\frac{8}{81}\).
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The Correct Answer is option 3 

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Last updated on Jun 23, 2025

-> The last date for CSIR NET Application Form 2025 submission has been extended to 26th June 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.

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