Answered: The pdf (probability density function)…

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.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.CR: Chapter 13 Review

Problem 22CR

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Question

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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