   # 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 5 e − x / 5 , [ 0 , ∞ ) ### 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 30RE
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 5 e − x / 5 , [ 0 , ∞ )

To determine

To graph: The function f(x)=15ex/5 using a graphing utility. Also determine whether the function f(x)=15ex/5 represents a probability density function over the interval [0,).

### Explanation of Solution

Given Information:

The function f(x)=15ex/5 over the interval [0,).

Graph:

Consider the provided function f(x)=15ex/5.

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=15ex/5.

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 bar graph of the function is obtained as,

Consider the provided function f(x)=15ex/5 over the interval [0,).

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

Consider any value x=5 in the interval [0,). Evaluate the function at x=5. So,

f(5)=15e5/5=15(e1)=0.36795=0.07358

So, the function f is continuous and nonnegative for all values on the interval [0,)

### 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 the integral. 47. 1tan2xsec2xdx

Calculus: Early Transcendentals

In Exercises 35-38, find an equation of the line that has slope m and y-intercept b. 36. m = 2; b = 1

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

Find the limit or show that it does not exist. limxarctan(ex)

Single Variable Calculus: Early Transcendentals

Writhe each number in scientific notation: 24.85

Elementary Technical Mathematics

Sketch the graph of each equation. (a) r=1sin (b) r=1sin(4)

Calculus: Early Transcendental Functions (MindTap Course List)

If A1 and A2 are the areas at the right then abf(x)dx= a) A1 A2 b) A1 + A2 c) A1 + A2 d) A1A2

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

Reminder Round all answers to two decimal places unless otherwise indicated. Defense SpendingData about recent ...

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

Self Check 6 Solve C=59(F32) for F

College Algebra (MindTap Course List) 