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The moment generating function (MGF) for a random variable X is: Mx (t) = E[eX]. Onc useful property of moment generating fu

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Answer #1

The Moment Generating function uniquely defines the distribution of a random variable.

So, for any unknown distribution, we calculate the moment generating function and compare them to a known Moment generating function(of known distributions).

If the calculated Moment generating function of the unknown distribution has the same form as that of the known MGF of some Known distribution, then the unknown distribution has the same probability distribution as that of the known distribution.

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