If moment generating function of continuous random variable X is λλt t < λ, then E(X3) equals to:

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SSC CGL Tier-II ( JSO ) 2021 Official Paper ( Held On: 10 August 2022 )
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  1. 8λ3
  2. 6λ3
  3. 4λ3
  4. 2λ3

Answer (Detailed Solution Below)

Option 2 : 6λ3
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Detailed Solution

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The correct answer is 6/λ3

Key Points

  • The moment generating function (MGF) of a random variable is a function that represents the expected values of its powers. 
    • The MGF of X is defined as M(t) = E(e^(tx)), where E represents the expected value.
    • The nth derivative of the MGF evaluated at t = 0 provides the expected value of X^n.

Additional Information

  • The condition -t < λ/λ ensures that the MGF of X exists and is finite.
  • The MGF is a useful tool to characterize the distribution of a random variable, and it provides a way to calculate its moments.

 Important Points

  • To calculate E(X^3) from the MGF of X, you need to take the third derivative of M(t) with respect to t, and then evaluate it at t = 0.
  • The MGF method assumes that the random variable X has a moment generating function, which may not be the case for all distributions.

 

 

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