Suppose that X is a continuous random variable with density function f. Show that E[|X - a|]

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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

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

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A First Course In Probability

ISBN: 9789332519077

9th Edition

Authors: Sheldon Ross

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Question Posted: Oct 22, 2015 03:03 AM

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Suppose that X is a continuous random variable with density function f. Show that E[|X - a|]

Question:

E[|X – al] = | x – alf(x) dx %3D

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Differentiating the above yield...View the full answer

A First Course In Probability

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