Question: 2. Suppose that X is a continuous random variable with density function f. Show that E[Xa] is minimized when a is equal to the median

2. Suppose that X is a continuous random variable with density function

f. Show that E[Xa] is minimized when a is equal to the median of F.

HINT: Write

$$E[X-a] = \int_{}^{} (x-a) f(x) dx$$

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

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