Chapter 5.3, Problem 38E

BuyFind*arrow_forward*

9th Edition

Jay L. Devore

ISBN: 9781305251809

Textbook Problem

There are two traffic lights on a commuter’s route to and from work. Let *X*_{1} be the number of lights at which the commuter must stop on his way to work, and *X*_{2} be the number of lights at which he must stop when returning from work. Suppose these two variables are independent, each with pmf given in the accompanying table (so *X*_{1}, *X*_{2} is a random sample of size *n* = 2).

x_{1} |
0 | 1 | 2 |

p(x)_{1} |
0.2 | 0.5 | 0.3 |

*µ* =1.1, σ^{2}=0.49

- a. Determine the pmf of
*T*=_{o}*X*_{1}+*X*_{2}. - b. Calculate
*µT*. How does it relate to_{o}*µ*, the population mean? - c. Calculate
*σ*^{2}*T*. How does it relate to_{o}*σ*^{2}, the population variance? - d. Let
*X*_{3}and*X*_{4}be the number of lights at which a stop is required when driving to and from work on a second day assumed independent of the first day. With*T*= the sum of all four_{o}*X*’s, what now are the values of_{i}*E*(*T*) and_{o}*V*(*T*)?_{o} - e. Referring back to (d), what are the values of
*P*(*T*= 8) and_{0}*P*(*T*≥ 7) [_{o}*Hint*: Don’t even think of listing all possible outcomes!]

**a.**

To determine

Find the pmf of

Explanation

**Given info:**

The random variables

**Calculation:**

*Independence of random variables:*

Two discrete random variables, *X* and *Y*, are said to be independent, if their joint pmf,

The distributions of

Thus, for each pair of value

For the pair of values (0, 0), the joint pmf is:

**b.**

To determine

Calculate

**c.**

To determine

Calculate

**d.**

To determine

Find the new values of

**e.**

To determine

Find the values of

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

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

Principles of Economics (MindTap Course List)

Brief Principles of Macroeconomics (MindTap Course List)

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Principles of Macroeconomics (MindTap Course List)

Principles of Microeconomics (MindTap Course List)

ECON: MICRO4 (New, Engaging Titles from 4LTR Press)

Fundamentals of Financial Management, Concise Edition (MindTap Course List)

Accounting Information Systems

Essentials of Business Communication (MindTap Course List)

Cornerstones of Financial Accounting

Fundamentals Of Financial Management, Concise Edition (mindtap Course List)

Foundations of Business (MindTap Course List)

Financial & Managerial Accounting

Corporate Financial Accounting

Fundamentals of Financial Management (MindTap Course List)

Essentials Of Statistics

Understanding Basic Statistics

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Statistics for The Behavioral Sciences (MindTap Course List)

Single Variable Calculus

Calculus: Early Transcendentals

Single Variable Calculus: Early Transcendentals, Volume I

Applied Calculus

Calculus (MindTap Course List)

Multivariable Calculus

Calculus (MindTap Course List)

Calculus: Early Transcendental Functions

Finite Mathematics and Applied Calculus (MindTap Course List)

Finite Mathematics

Intermediate Algebra

Precalculus: Mathematics for Calculus (Standalone Book)

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Calculus: An Applied Approach (MindTap Course List)

Mathematical Excursions (MindTap Course List)

Trigonometry (MindTap Course List)

Elements Of Modern Algebra

Mathematical Applications for the Management, Life, and Social Sciences

Elementary Geometry For College Students, 7e

Contemporary Mathematics for Business & Consumers

Elementary Technical Mathematics

Finite Mathematics for the Managerial, Life, and Social Sciences

Calculus: Early Transcendental Functions (MindTap Course List)

Single Variable Calculus: Early Transcendentals

Calculus of a Single Variable