Probability and Statistics for Eng...

9th Edition

Jay L. Devore

ISBN: 9781305251809

Textbook Problem

The number of customers waiting for gift-wrap service at a department store is an rv X with possible values 0, 1, 2,3, 4 and corresponding probabilities .1, .2, .3, .25, .15. A randomly selected customer will have 1, 2, or 3 packages for wrapping with probabilities .6, .3, and .1, respectively. Let Y = the total number of packages to be wrapped for the customers waiting in line (assume that the number of packages submitted by one customer is independent of the number submitted by any other customer).

a. Determine P(X = 3, Y = 3), i.e., p(3, 3).

b. Determine p(4, 11).

To determine

Find P(X=3,Y=3), that is, p(3,3).

Explanation

Given info:

The random variables are X and Y. X is the number of customers waiting for gift-wrap service, with possible values 0, 1, 2, 3 and 4 with corresponding probabilities 0.1, 0.2, 0.3, 0.25 and 0.15. Y is the total number of packages to be wrapped for the customers waiting in line, where each customer may have 1, 2 or 3 packages to be wrapped with respective probabilities 0.6, 0.3 and 0.1. The number of packages for one customer is independent of that of the other.

Calculation:

The probability P(X=3,Y=3) or p(3,3) is the probability that “there are X=3 customers waiting for the gift-wrap service” and “a total of Y=3 packages are to be wrapped for the customers waiting in line”.

It is known that each waiting customer has either 1 or 2 or 3 packages to be wrapped.

Thus, there will be 3 customers waiting in line and a total of 3 packages waiting to be wrapped, if each of the three waiting customers has exactly 1 package to be wrapped.

Thus,

P(X=3,Y=3)=p(3,3)=P(3 customers having 1 package each)=P(

To determine

Find p(4,11).

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Chapter 5 Solutions

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Sect-5.1 P-1E Sect-5.1 P-2E Sect-5.1 P-3E Sect-5.1 P-4E Sect-5.1 P-5E Sect-5.1 P-6E Sect-5.1 P-7E Sect-5.1 P-8E Sect-5.1 P-9E Sect-5.1 P-10E

Sect-5.1 P-11E Sect-5.1 P-12E Sect-5.1 P-13E Sect-5.1 P-14E Sect-5.1 P-15E Sect-5.1 P-16E Sect-5.1 P-17E Sect-5.1 P-18E Sect-5.1 P-19E Sect-5.1 P-20E Sect-5.1 P-21E Sect-5.2 P-22E Sect-5.2 P-23E Sect-5.2 P-24E Sect-5.2 P-25E Sect-5.2 P-26E Sect-5.2 P-27E Sect-5.2 P-28E Sect-5.2 P-29E Sect-5.2 P-30E Sect-5.2 P-31E Sect-5.2 P-32E Sect-5.2 P-33E Sect-5.2 P-34E Sect-5.2 P-35E Sect-5.2 P-36E Sect-5.3 P-37E Sect-5.3 P-38E Sect-5.3 P-39E Sect-5.3 P-40E Sect-5.3 P-41E Sect-5.3 P-42E Sect-5.3 P-43E Sect-5.4 P-46E Sect-5.4 P-47E Sect-5.4 P-48E Sect-5.4 P-49E Sect-5.4 P-50E Sect-5.4 P-51E Sect-5.4 P-52E Sect-5.4 P-53E Sect-5.4 P-54E Sect-5.4 P-55E Sect-5.4 P-56E Sect-5.4 P-57E Sect-5.5 P-58E Sect-5.5 P-59E Sect-5.5 P-60E Sect-5.5 P-61E Sect-5.5 P-62E Sect-5.5 P-63E Sect-5.5 P-64E Sect-5.5 P-65E Sect-5.5 P-66E Sect-5.5 P-67E Sect-5.5 P-68E Sect-5.5 P-69E Sect-5.5 P-70E Sect-5.5 P-71E Sect-5.5 P-72E Sect-5.5 P-73E Sect-5.5 P-74E Ch-5 P-75SE Ch-5 P-76SE Ch-5 P-77SE Ch-5 P-78SE Ch-5 P-79SE Ch-5 P-80SE Ch-5 P-81SE Ch-5 P-82SE Ch-5 P-83SE Ch-5 P-84SE Ch-5 P-85SE Ch-5 P-86SE Ch-5 P-87SE Ch-5 P-88SE Ch-5 P-89SE Ch-5 P-90SE Ch-5 P-91SE Ch-5 P-92SE Ch-5 P-93SE Ch-5 P-94SE Ch-5 P-95SE Ch-5 P-96SE Ch-5 P-97SE Ch-5 P-98SE

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Probability and Statistics for Eng...

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Statistics Probability and Statistics for Engineering and the Sciences 9th Edition