Question: Suppose that X is a continuous random variable with density function f. Show that E[|X - a|] is minimized when a is equal to the

Suppose that X is a continuous random variable with density function f. Show that E[|X - a|] is minimized when a is equal to the median of F.
Write
E[|X – al] = | x – alf(x) dx %3D

Now break up the integral into the regions where x a, and differentiate.

E[|X al] = | x alf(x) dx %3D

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