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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 9.1, Problem 28E
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

Solutions

Chapter
Section
Problem 1CP
Problem 2CP
Problem 3CP
Problem 4CP
Problem 5CP
Problem 6CP
Problem 1SWU
Problem 2SWU
Problem 3SWU
Problem 4SWU
Problem 5SWU
Problem 6SWU
Problem 7SWU
Problem 8SWU
Problem 9SWU
Problem 10SWU
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Finding Mean, Variance, and Standard Deviation In Exercises 27 and 28, find the mean, variance, and standard deviation of the discrete random variable x. See Examples 4, 5, and 6.

Die Roll x is (a) the number of points when a four-sided die is rolled once and (b) the sum of the points when the four-sided die is rolled twice.

(a)

To determine

To calculate: The mean, variance and standard deviation of the number of points when a four-sided die is rolled once.

Explanation

Given Information:

A four-sided dice is rolled once.

Formula used:

The probability of random variable is given by

P(x)=Frequency of xTotal number of outcomes

The expected value or the mean of the random variable of the set of values of the discrete random variable consisting of m different values is given by

Mean=x1P(x1)+x2P(x2)+...+xmP(xm)

The variance is given by

V(x)=(x1−μ)2P(x1)+(x2−μ)2P(x2)+...+(xm−μ)2P(xm)

And the standard deviation is given by

σ=V(x)

Calculation:

Consider the statement,

A four-sided dice is rolled once.

Let S be the sample space. Then, S={1,2,3,4}.

So, number of possible outcomes is 4.

Frequency of each possible outcome is,

Random variable,x1234Frequency of x, n(x)1111

Then the probability of getting a number 1 will be

P(x1)=Frequency of x1Total number of outcomes=116

The probability of getting a number 2 will be

P(x2)=Frequency of x2Total number of outcomes=116

The probability of getting a number 3 will be

P

(b)

To determine

To calculate: The mean, variance and the standard deviation of sum of the points when a four-sided die is rolled twice.

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Sect-9.1 P-1CPSect-9.1 P-2CPSect-9.1 P-3CPSect-9.1 P-4CPSect-9.1 P-5CPSect-9.1 P-6CPSect-9.1 P-1SWUSect-9.1 P-2SWUSect-9.1 P-3SWUSect-9.1 P-4SWU
Sect-9.1 P-5SWUSect-9.1 P-6SWUSect-9.1 P-7SWUSect-9.1 P-8SWUSect-9.1 P-9SWUSect-9.1 P-10SWUSect-9.1 P-1ESect-9.1 P-2ESect-9.1 P-3ESect-9.1 P-4ESect-9.1 P-5ESect-9.1 P-6ESect-9.1 P-7ESect-9.1 P-8ESect-9.1 P-9ESect-9.1 P-10ESect-9.1 P-11ESect-9.1 P-12ESect-9.1 P-13ESect-9.1 P-14ESect-9.1 P-15ESect-9.1 P-16ESect-9.1 P-17ESect-9.1 P-18ESect-9.1 P-19ESect-9.1 P-20ESect-9.1 P-21ESect-9.1 P-22ESect-9.1 P-23ESect-9.1 P-24ESect-9.1 P-25ESect-9.1 P-26ESect-9.1 P-27ESect-9.1 P-28ESect-9.1 P-29ESect-9.1 P-30ESect-9.1 P-31ESect-9.1 P-32ESect-9.1 P-33ESect-9.1 P-35ESect-9.1 P-36ESect-9.1 P-37ESect-9.1 P-38ESect-9.2 P-1CPSect-9.2 P-2CPSect-9.2 P-3CPSect-9.2 P-4CPSect-9.2 P-5CPSect-9.2 P-1SWUSect-9.2 P-2SWUSect-9.2 P-3SWUSect-9.2 P-4SWUSect-9.2 P-5SWUSect-9.2 P-6SWUSect-9.2 P-7SWUSect-9.2 P-1ESect-9.2 P-2ESect-9.2 P-3ESect-9.2 P-4ESect-9.2 P-5ESect-9.2 P-6ESect-9.2 P-7ESect-9.2 P-8ESect-9.2 P-9ESect-9.2 P-10ESect-9.2 P-11ESect-9.2 P-12ESect-9.2 P-13ESect-9.2 P-14ESect-9.2 P-15ESect-9.2 P-16ESect-9.2 P-17ESect-9.2 P-18ESect-9.2 P-19ESect-9.2 P-20ESect-9.2 P-21ESect-9.2 P-22ESect-9.2 P-23ESect-9.2 P-24ESect-9.2 P-25ESect-9.2 P-26ESect-9.2 P-27ESect-9.2 P-28ESect-9.2 P-29ESect-9.2 P-30ESect-9.2 P-31ESect-9.2 P-32ESect-9.2 P-33ESect-9.2 P-34ESect-9.2 P-35ESect-9.2 P-36ESect-9.2 P-37ESect-9.2 P-38ESect-9.2 P-39ESect-9.3 P-1CPSect-9.3 P-2CPSect-9.3 P-3CPSect-9.3 P-4CPSect-9.3 P-5CPSect-9.3 P-6CPSect-9.3 P-7CPSect-9.3 P-1SWUSect-9.3 P-2SWUSect-9.3 P-3SWUSect-9.3 P-4SWUSect-9.3 P-5SWUSect-9.3 P-6SWUSect-9.3 P-1ESect-9.3 P-2ESect-9.3 P-3ESect-9.3 P-4ESect-9.3 P-5ESect-9.3 P-6ESect-9.3 P-7ESect-9.3 P-8ESect-9.3 P-9ESect-9.3 P-10ESect-9.3 P-11ESect-9.3 P-12ESect-9.3 P-13ESect-9.3 P-14ESect-9.3 P-15ESect-9.3 P-16ESect-9.3 P-17ESect-9.3 P-18ESect-9.3 P-19ESect-9.3 P-20ESect-9.3 P-21ESect-9.3 P-22ESect-9.3 P-23ESect-9.3 P-24ESect-9.3 P-25ESect-9.3 P-26ESect-9.3 P-27ESect-9.3 P-28ESect-9.3 P-29ESect-9.3 P-30ESect-9.3 P-31ESect-9.3 P-32ESect-9.3 P-33ESect-9.3 P-34ESect-9.3 P-35ESect-9.3 P-36ESect-9.3 P-37ESect-9.3 P-38ESect-9.3 P-39ESect-9.3 P-40ESect-9.3 P-41ESect-9.3 P-42ESect-9.3 P-43ESect-9.3 P-44ESect-9.3 P-45ESect-9.3 P-46ESect-9.3 P-47ESect-9.3 P-48ESect-9.3 P-49ESect-9.3 P-50ESect-9.3 P-54ESect-9.3 P-55ESect-9.3 P-56ESect-9.3 P-57ECh-9 P-1RECh-9 P-2RECh-9 P-3RECh-9 P-4RECh-9 P-5RECh-9 P-6RECh-9 P-7RECh-9 P-8RECh-9 P-9RECh-9 P-10RECh-9 P-11RECh-9 P-12RECh-9 P-13RECh-9 P-14RECh-9 P-15RECh-9 P-16RECh-9 P-17RECh-9 P-18RECh-9 P-19RECh-9 P-20RECh-9 P-21RECh-9 P-22RECh-9 P-23RECh-9 P-24RECh-9 P-25RECh-9 P-26RECh-9 P-27RECh-9 P-28RECh-9 P-29RECh-9 P-30RECh-9 P-31RECh-9 P-32RECh-9 P-33RECh-9 P-34RECh-9 P-35RECh-9 P-36RECh-9 P-37RECh-9 P-38RECh-9 P-39RECh-9 P-40RECh-9 P-41RECh-9 P-42RECh-9 P-43RECh-9 P-44RECh-9 P-45RECh-9 P-46RECh-9 P-47RECh-9 P-48RECh-9 P-49RECh-9 P-50RECh-9 P-51RECh-9 P-52RECh-9 P-53RECh-9 P-54RECh-9 P-55RECh-9 P-56RECh-9 P-57RECh-9 P-58RECh-9 P-59RECh-9 P-60RECh-9 P-61RECh-9 P-62RECh-9 P-1TYSCh-9 P-2TYSCh-9 P-3TYSCh-9 P-4TYSCh-9 P-5TYSCh-9 P-6TYSCh-9 P-7TYSCh-9 P-8TYSCh-9 P-9TYSCh-9 P-10TYSCh-9 P-11TYSCh-9 P-12TYSCh-9 P-13TYSCh-9 P-14TYSCh-9 P-15TYSCh-9 P-16TYS

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