If X is a Binomial random variable with parameter (n, p), where 0< p <1, then as k goes from 0 ton, P(X = k) first increase monotonically and then decrease monotonically, reaching its largest values. Show that k is the largest integer which is less than or equal to (n+1) p. (Hint: P(X = k) / P(X = k − 1).) Using the relationship obtained in (a), find P(X=0), P(X = 1) and P(X=2) for X~ Binomial(6,0.4).

If X is a Binomial random variable with parameter (n, p), where 0< p <1, then as k goes from 0 ton, P(X = k) first increase monotonically and then decrease monotonically, reaching its largest values. Show that k is the largest integer which is less than or equal to (n+1) p. (Hint: P(X = k) / P(X = k − 1).) Using the relationship obtained in (a), find P(X=0), P(X = 1) and P(X=2) for X~ Binomial(6,0.4).

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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