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= k} is nonincreasing in k = 1,2, ..., prove that E[X] P{X = k} < 2° k be a nonnegative continuous random variable having a creasing density function. Show that 2E[X] f(x) < x2 for all x > 0

= k} is nonincreasing in k = 1,2, ..., prove that E[X] P{X = k} < 2° k be a nonnegative continuous random variable having a creasing density function. Show that 2E[X] f(x) < x2 for all x > 0

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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a. Let X be a discrete random variable whose possible values are 1,2, .... If P{X = k} is nonincreasing in k = 1,2, ..., prove that E[X] P{X = k} < 2 k? b. Let X be a nonnegative continuous random variable having a nonincreasing density function. Show that 2E[X] f(x) < x2 for all x > 0
Transcribed Image Text:a. Let X be a discrete random variable whose possible values are 1,2, .... If P{X = k} is nonincreasing in k = 1,2, ..., prove that E[X] P{X = k} < 2 k? b. Let X be a nonnegative continuous random variable having a nonincreasing density function. Show that 2E[X] f(x) < x2 for all x > 0
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