Let X be a continuous random variable with density function f . Recall that the median of
Question:
Let X be a continuous random variable with density function f . Recall that the median of the distribution of X is the real number m such that P(X ≤ m) = P(X ≥ m).
Show that, if the distribution of X is symmetric around a point a (see Exercise 21 of Section 6.1), and the expectation E(X) exists, then m = E(X) = a.
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Related Book For
Introduction To Probability Volume 2
ISBN: 9781118123331
1st Edition
Authors: Narayanaswamy Balakrishnan, Markos V. Koutras, Konstadinos G. Politis
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