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  • one year ago

Let the probability function of X be given by f(x)= ce^(-x) , x=1,2,3, ... How to find the moment generating function of X and its E(X)?

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  1. mathmate
    • one year ago
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    Let X = random variable, t = a dummy variable, f(x)=pdf of discrete random variable X Moment generating function, \(M_X(t)\) \(=E[e^{tX}]\) (expected value of e^(tX)) \(=\sum_{-\infty}^\infty e^{tx}f(x)dx\) (note: limits of summation cover the actual domain of f(x), in this case, sum from 1 to \(\infty\) ) E(X) is just \(M_X(0)\) once you have found \(M_X(t)\). For more theoretical background, read for example: https://en.wikipedia.org/wiki/Moment-generating_function

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