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The pdf (probability density function) of a random variable X, px(x), has the following property: px(x) = 0, for x < 0. Show that, for any a > 0, P(X >a) < X, where µx E[X] denotes the mean.

The pdf (probability density function) of a random variable X, px(x), has the following property: px(x) = 0, for x < 0. Show that, for any a > 0, P(X >a) < X, where µx E[X] denotes the mean.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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The pdf (probability density function) of a random variable X, px(x), has the following property: px(x) = 0, for x < 0. Show that, for any a > 0, P(X >a) < X, where µx E[X] denotes the mean.
Transcribed Image Text:The pdf (probability density function) of a random variable X, px(x), has the following property: px(x) = 0, for x < 0. Show that, for any a > 0, P(X >a) < X, where µx E[X] denotes the mean.
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