   # Finding Expected Value, Variance, and Standard Deviation In Exercises 39-44, use the given probability density function over the indicated interval to find the (a) expected value, (b) variance, and (c) standard deviation of the random variable. (d) Then sketch the graph of the probability density function and locate the mean on the graph. f ( x ) = x 72 , [ 0 , 12 ] ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
Publisher: Cengage Learning
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
Publisher: Cengage Learning
ISBN: 9781305860919
Chapter 9, Problem 40RE
Textbook Problem
1 views

## Finding Expected Value, Variance, and Standard Deviation In Exercises 39-44, use the given probability density function over the indicated interval to find the (a) expected value, (b) variance, and (c) standard deviation of the random variable. (d) Then sketch the graph of the probability density function and locate the mean on the graph. f ( x ) = x 72 , [ 0 , 12 ]

(a)

To determine

To calculate: The expected value of probability density function f(x)=x72 over the interval [0,12].

### Explanation of Solution

Given Information:

The probability density function is defined as

f(x)=x72 over the interval [0,12].

Formula used:

For any probability density function f of a continuous random variable x over the interval [a,b], the expected value of x is defined as,

μ=E(x)=abxf(x) dx

The integration formula,

xndx=xn+1n+1+C

Where, n is any real number and C is a constant.

The Fundamental theorem,

abf(x) dx=F(b)F(a)

Calculation:

Consider the provided probability density function.

f(x)=x72 over the interval [0,12].

Use the formula E(x)=abxf(x) dx for the provided probability density function to calculate the expected value

(b)

To determine

To calculate: The variance of probability density function f(x)=x72 over the interval [0,12].

(c)

To determine

To calculate: The standard deviation of probability density function f(x)=x72 over the interval [0,12].

(d)

To determine

To graph: The probability density function f(x)=x72 over the interval [0,12].

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Find more solutions based on key concepts
Other Equations Find all real solutions of the equation. 93. 5=4x3

Precalculus: Mathematics for Calculus (Standalone Book)

Evaluate the indefinite integral. x1x2dx

Calculus: Early Transcendentals

Convert the expressions in Exercises 6584 to power form. 2x3x0.12+43x1.1

Finite Mathematics and Applied Calculus (MindTap Course List)

In Exercises 89-94, determine whether the statement is true or false. If it is true, explain why it is true. If...

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

Find f if f(x)=x2,x0,f(1)=0, and f(2)=0.

Calculus (MindTap Course List)

In problems 27-30, find. 28.

Mathematical Applications for the Management, Life, and Social Sciences

Find each product. 4(a+6)

Elementary Technical Mathematics

Find the area of the triangle in Problem 5.

Trigonometry (MindTap Course List)

The area of the parallelogram at the right is: 26

Study Guide for Stewart's Multivariable Calculus, 8th

Sometimes, Always, or Never: If 0 ≤ an ≤ bn for all n and diverges, then converges.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Explain what is meant by the concept that main effects and interactions are independent.

Research Methods for the Behavioral Sciences (MindTap Course List) 