   # 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 ) = 3 16 x , [ 0 , 4 ] ### 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 44RE
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 ) = 3 16 x ,     [ 0 , 4 ]

(a)

To determine

To calculate: The expected value of probability density function f(x)=316x over the interval [0,4].

### Explanation of Solution

Given Information:

The probability density function is, f(x)=316x over the interval [0,4].

Formula used:

The expected value E(x) of a probability density function f for a continuous random variable x over the interval [a,b] is,

μ=E(x)=abxf(x) dx

The simple power rule of integration,

xndx=xn+1n+1+C

The Fundamental theorem of calculus for definite integral of a function f on a closed interval [a,b] is,

abf(x)dx=F(b)F(a).

Calculation:

Consider the provided probability density function, f(x)=316x.

Use the definition of expected value for the provided probability density function,

E(x)=abxf(x) dx

Substitute 0 for a, 4 for b and 316x for f(x)

(b)

To determine

To calculate: The variance of probability density function f(x)=316x over the interval [0,4].

(c)

To determine

To calculate: The standard deviation of probability density function f(x)=316x over the interval [0,4].

(d)

To determine

To graph: The probability density function f(x)=316x over the interval [0,4].

### 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
Solve the equations in Exercises 126. 6x(x2+1)2(x2+2)48x(x2+1)3(x2+2)3(x2+2)8=0

Finite Mathematics and Applied Calculus (MindTap Course List)

Worker Efficiency An efficiency study conducted for Elektra Electronics showed that the number of Space Command...

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

16. If , find the following. (a) (b) (c)

Mathematical Applications for the Management, Life, and Social Sciences

Prove the following identities. cos22=tan+sin2tan

Trigonometry (MindTap Course List)

A differential equation is separable if it can be written in the form: a) dydx=f(x)+g(y) b) dydx=f(g(x,y)) c) d...

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

Exercises Solve each equation for x. lnx+3=ln-5x+51

College Algebra (MindTap Course List)

Identify the threats to internal validity for pre-post designs.

Research Methods for the Behavioral Sciences (MindTap Course List) 