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.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For  book-img-for-question

Introduction To Probability Volume 2

ISBN: 9781118123331

1st Edition

Authors: Narayanaswamy Balakrishnan, Markos V. Koutras, Konstadinos G. Politis

Question Posted: