Explain the term Moments Generating Function.
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Moment generating functions are useful for several reasons, one of which is their application to analysis of sums of random variables. Before discussing MGFs, let's define moments. Definition . The nth moment of a random variable is defined to be E [ X n ] . ... For example, the first moment is the expected value .
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In probability theory and statistics, the moment-generating function of a real-valued random variable is an alternative specification of its probability distribution. ... There are particularly simple results for the moment-generating functions of distributions defined by the weighted sums of random variables
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