If moment generating function of continuous random variable X is \(\frac{λ}{λ-t}\) t < λ, then E(X³) equals to:

Question

Question

This question was previously asked in

SSC CGL Tier-II ( JSO ) 2021 Official Paper ( Held On: 10 August 2022 )

Answer 1

The correct answer is \(6/λ^3\)

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.