Uniform Distribution Expected Value

[redskins187]

Homework Statement

If X~(-5,5) find E[||X|-2|]

Homework Equations

If a variable is distributed uniformly then f(x) = 1 / (b-a), with a mean of (a+b)/2.
If x~u, then y~u.

The Attempt at a Solution

I think I should change the variable, so y = |X| - 2, and then find E[|y|]. So if I do that, I change the integration from -5 and 5 to 3 and 3 because |-5| - 2 = |5| - 2. Wouldn't that just be zero, or do I have my integration points wrong?

I am also confused about finding the expected value of an absolute of something. Should I do two separate integrals, one with integral (-y * f(y) * dy) and the other integral (y * f(y) * dy) or how should I handle the absolute value sign?

I'm pretty confused by this problem, any help would be greatly appreciated!

 

[jbunniii]

Try expressing the function piecewise without absolute values. The first step would be:

$$||x| - 2| = \begin{cases}<br /> |x| - 2 & \textrm{if } |x| \geq 2 \\<br /> -|x| + 2 & \textrm{otherwise}<br /> \end{cases}$$

Now repeat the procedure for each of the two cases. You will end up with four "pieces" which you can integrate individually and sum the results.