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Chapter 6: Q.6.12 (page 271)

The number of people who enter a drugstore in a given hour is a Poisson random variable with parameter 位 = 10. Compute the conditional probability that at most 3 men entered the drugstore, given that 10 women entered in that hour. What assumptions have you made?

Short Answer

Expert verified

The conditional probability that at most 3 men entered the drugstore is 0.2650

Step by step solution

01

Content Introduction

The number of people who enter a drugstore in a given hour is a Poisson random variable with parameter 位 = 10 .

Let X denote the number of people who enter a drugstore in given hour.

02

Content Explanation

The probability density function of the Poisson distribution as shown below:

P(x)=e-位p(位p)ii!

Let us assume that men and women are equally likely to come yo the store, which means p=12

Finding conditional probability that at most 3 men entered the drugstore given that 10 women in that one hour is:


localid="1647268885382" role="math" P[X鈮�3M鈭�X=10W]P[X鈮�3M鈭�X=10W]=P(鈮�3M鈭�10W)P(10W),(X=10W)P(X=10W)=e-位p(位p)xx!=e-5(5)1010!P(X鈮�3M鈭�X=10W)P(X鈮�3M鈭�X=10W)=P(0M,10W)+P(1M,10W)++P(3M,10W)P(2M,10W)=e-5(5)1010!脳e-5(5)00!+(5)11!+(5)22!+(5)33!=e-10(5)1010![1+5+12.5+20.833]=e-10(5)1010![39.3333]P[X鈮�3M鈭�X=10W]=39.3333e-5=0.2650

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