   # Identifying Probability Density Functions In Exercises 25-30, use a graphing utility to graph the function. Then determine whether the function f represents a probability density function over the given interval. If f is not a probability density function, identify the condition(s) that is (are) not satisfied. f ( x ) = 1 8 e − x / 8 , [ 0 , 8 ] ### 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 29RE
Textbook Problem
1 views

## Identifying Probability Density Functions In Exercises 25-30, use a graphing utility to graph the function. Then determine whether the function f represents a probability density function over the given interval. If f is not a probability density function, identify the condition(s) that is (are) not satisfied. f ( x ) = 1 8 e − x / 8 ,        [ 0 , 8 ]

To determine

To graph: The function using a graphing utility and determine whether the function f(x)=18ex/8 represents a probability density function over the interval [0,8].

### Explanation of Solution

Given Information:

The function f(x)=18ex/8 over the interval [0,8].

Graph:

Consider the provided function f(x)=18ex/8.

Use the ti-83 graphing calculator to construct the graph of the function.

Step 1: Open the ti-83 graphing calculator.

Step 2: Press [y=] and enter the function Y1=18ex/8.

Step 3: Press the [window] key and adjust the scale.

Xmin=0Xmax=8Xscl=1

And,

Ymin=0Ymax=0.25Yscl=0.01

Step 4: Press the [graph] key.

The graph of the function f(x)=18ex/8 is obtained as,

Consider the provided function f(x)=18ex/8 over the interval [0,8].

A function f of a continuous random variable x in the interval [a,b] is a probability density function if it is nonnegative and continuous on the interval [a,b].

And,

abf(x) dx=1

For x=8 in the interval [0,8], the function is evaluated as,

f(8)=18e8/8=18e1=0.367980.046

The function f is continuous and nonnegative for all values on the interval [0,8].

Since, the provided function is a constant function and so the function f is continuous and nonnegative for all values on the interval [0,8].

Now, show that abf(x) dx=1

### 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
Evaluate Evaluate the expression. 10. 5|104|

Precalculus: Mathematics for Calculus (Standalone Book)

In Exercises 23-32, determine whether the statement is true or false. Give a reason for your choice. 27. 24x13x...

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

In Problems 27 and 28, find the slope of the line that passes through each pair of points. 28. and

Mathematical Applications for the Management, Life, and Social Sciences

Simplify: (6y35y2y+2)(2y1)

Elementary Technical Mathematics

Given the table of function values below, which of the following is the best estimate for the instantaneous rat...

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

Rewritten in reverse order,

Study Guide for Stewart's Multivariable Calculus, 8th 