Let X follow a binomial distribution. Show that Var[X] ≤ E[X]

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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Let X follow a binomial distribution. Show that Var[X] ≤ E[X].

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Step 1

Let us consider X follow a binomial distribution with parameter n & p, then

X~Bin(n,p) 

We know that both 0p,q≤ 1

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