Solutions - 5150-01

(1) Recall formula for expectation of a continuous random variable:

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(2) Use formula to find an equation relating and :

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(3) Integrate the PDF to get a second equation:

Since integrating a PDF should yield :

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(4) Solve system of equations for and :

Isolating in the second equation yields .

Plugging this into the first equation yields .

Solving for yields , and thus .

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(5) Compute variance:

Using , first compute :

So: