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**Problem**

Let X be a uniform(0,1) random variable, and let Y=e^−X.

Find the CDF of Y.

Find the PDF of Y.

Find EY.

**Relevant Equations**

http://puu.sh/kAVJ8/0f2b1e7b22.png [Broken]

http://puu.sh/kAVJ8/0f2b1e7b22.png [Broken]

**My attempt at a solution**

If I solve for the range of y I get (1, 1/e), but because Y is not an increasing function, my second bound is smaller than my first. I am really confused as to how I would be able to solve for the CDF and PDF in this case... Any help would be greatly appreciated.

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