/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q.6.12 The number of people who enter a... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

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

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Suppose that n points are independently chosen at random on the circumference of a circle, and we want the probability that they all lie in some semicircle. That is, we want the probability that there is a line passing through the center of the circle such that all the points are on one side of that line, as shown in the following diagram:

Let P1, ... ,Pn denote the n points. Let A denote the event that all the points are contained in some semicircle, and let Ai be the event that all the points lie in the semicircle beginning at the point Pi and going clockwise for 180鈼�, i = 1, ... , n.

(a) Express A in terms of the Ai.

(b) Are the Ai mutually exclusive?

(c) Find P(A).

If X and Y are independent standard normal random variables, determine the joint density function of

U=XV=XY

Then use your result to show that X/Yhas a Cauchy distribution.

If X and Y are independent random variables both uniformly distributed over (0,1), find the joint density function of R=X2+Y2,胃=tan-1Y/X.

Suppose X and Y are both integer-valued random variables. Let p(i|j) = P(X = i|Y = j) and q(j|i) = P(Y = j|X = i) Show that P(X = i, Y = j) = p(i|j)  i p(i|j) q(j|i

Jill鈥檚 bowling scores are approximately normally distributed with mean 170and standard deviation 20, while Jack鈥檚 scores are approximately normally distributed with mean 160and standard deviation 15. If Jack and Jill each bowl one game, then assuming that their scores are independent random variables, approximate the probability that

(a) Jack鈥檚 score is higher;

(b) the total of their scores is above 350
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.