Question
Download Solution PDFIf moment generating function of continuous random variable X is \(\frac{λ}{λ-t}\) t < λ, then E(X3) equals to:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFKey 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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