(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let X be a continuous random variable with median m.

Minimize E[|X - b|] as a function of b. Hint: Show that E[|X - b|] = E[|X - m|] + 2 [tex]\int[/tex] (x - b) f(x) dx , where the integral is from b to m.

2. Relevant equations

3. The attempt at a solution

I wanted to try a solution but I even don't know how to determine whether it is minimum or not. Please help.

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# Homework Help: Minimize expected value of the absolute difference

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