A random variable X has moment generating function m(t)=(5+exp(2t))/6. What is the variance of X?

Question

A random variable X has moment generating function m(t)=(5+exp(2t))/6. What is the variance of X?
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Solution 1

The moment generating function (MGF) of a random variable X is a function that generates the moments of the distribution of X. The nth moment of X is given by the nth derivative of the MGF evaluated at t=0.

The mean (first moment) of X is given by the first derivative of the MGF evaluated at t=0. T Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
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