Question
Download Solution PDFIf moment generating function of discrete random variable X is (q + pet)n, then E(X2) equal to
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe 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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