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How do you find the expected probability from the density function f(x) = e^-x?

The density function of a random variable X is

f(x) = e^-x x >= 0
= 0 otherwise

Find (a) E(X), (b) E(X²), (c) E{(X-1)²}.

Please see attached for full question.

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Solution Summary

This solutions provides step-by-step calculations for integrating the density function to find the area under the curve in an attached Word document.