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Moment Generating Function

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What is the moment generating function of the probability density function f(x) = 4x-x^2 for 0<x<2? I know it has something to do with E(e^tx) in other words integrate over 2 to 0 e^tx (4x - x^2) dx, but I don't know how to do it.

How do I use this to find the mean and variance of this distribution? (somebody mentioned Taylor decomposition but I don't know what that is)


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Solution Summary

The determination of the Moment Generating Function of a probability density function is discussed in the solution.

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Moment Generating Functions

Can you please explain me how I can use the moment generating functions to find the limiting distribution:
Suppose that Zi for N(0,1) and that Z1, Z2,...are independent. Use moment generating functions to find the limiting distribution of... (see attached file).

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