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You have a continuous random variable X and have gone to the trouble of calculating its generating function: GX[t] = Expect[E^(t X)] = Integrate[E^(t x) pdf[x], {x, Xlow, Xhigh}]

Explain this:

If a and b are constants, then the generating function of (a X + b) is:

E^(b t) GX[a t]

?• Is the same thing true for discrete random variables?

Could someone help me with this? Not sure how to explain.

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