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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)
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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If X is a Binomial random variable with parameter (n, p), where 0< p <1, then as k goes from 0 to n, 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).
Transcribed Image Text:If X is a Binomial random variable with parameter (n, p), where 0< p <1, then as k goes from 0 to n, 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).
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For part b

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. (a) Show that k is the largest integer which is less than or equal to (n+1)p. (Hint: You may use P(X = k) / P(X = k − 1).) (b) Using the relationship obtained in (a), find P(X = 0), P(X = 1) and P(X=2) for X ~ Binomial(6,0.4).
Transcribed Image Text: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. (a) Show that k is the largest integer which is less than or equal to (n+1)p. (Hint: You may use P(X = k) / P(X = k − 1).) (b) Using the relationship obtained in (a), find P(X = 0), P(X = 1) and P(X=2) for X ~ Binomial(6,0.4).
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