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This question was created from HW1 https://www.coursehero.com/file/23859296/HW1/ The moment generating Function is defined as: Vx(t) = E(e^Xt) = Sum of all x(e^xt)P(X=x) or Vx(t) = E(e^Xt) = integral from -inf to +inf (e^Xt fx(x) dx if X is discrete of continuous respectively (c) Show that if the random variables X and Y are independent and Z = X +Y, then 1,!) Z (t) = 1px(t)1/)y(t).
Hint: you have to use the fact that if two random variables X and Y are independent and f and g are
two functions, then the two new random variables U = f (X) and V = g(Y) are also independent.

This problem can be easily solved using the fact that... View the full answer

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