If moment generating function of discrete random variable X is (q + pet)n, then E(X2) equal to

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SSC CGL Tier-II ( JSO ) 2021 Official Paper ( Held On: 10 August 2022 )
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  1. nq(np + q)
  2. np(p + nq)
  3. nq(p + nq)
  4. np(np + q)

Answer (Detailed Solution Below)

Option 4 : np(np + q)
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PYST 1: SSC CGL - English (Held On : 11 April 2022 Shift 1)
25 Qs. 50 Marks 12 Mins

Detailed Solution

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The correct answer is np(np + q).


Key Points

  • A moment generating function is a mathematical tool that helps to calculate moments of a distribution (i.e. its mean, variance, etc.).
  • In this case, the moment generating function of X is given by (q + pet)^n.
  • To find the expected value of X^2, we can use the second derivative of the moment generating function and evaluate it at q = 0.

 Additional Information

  • Moment generating functions are not always unique for a given distribution.
  • The expected value of X^2 can also be found by directly calculating E(X^2) from the definition of expectation.

 Important Points

  • Moment generating functions can be useful in cases where it is difficult to directly calculate moments of a distribution.
  • The moment generating function can provide information about all the moments of a distribution.

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