## anonymous 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)?

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