   Chapter 9.2, Problem 6E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

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

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
3 views

# Verifying a Probability Density Function In Exercises 1-6, show that the function is a probability density function over the given interval. See Examples 1 and 2. f ( x ) = 0.2 e − 0.2 x , ( 0 , ∞ )

To determine

To prove: The function, f(x)=0.2e0.2x is a probability density function over the interval [0,).

Explanation

Given Information:

The function, f(x)=0.2e0.2x over the interval [0,).

Proof:

Consider the function,

f(x)=0.2e0.2x

A function f of a continuous random variables x whose set of values is the interval [a,b]. The function is a probability density function when it is non-negative and continuous on the interval [a,b] and when

abf(x)dx=1

f(x) is non-negative and continuous over the interval [0,)

Now, evaluate abf(x)dx as,

0f(x)dx=00.2e0.2xdx=0.20e0.2xdx=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

#### 2x2 + 8x + 7 = 0

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

#### Evaluate i=1n32i1.

Single Variable Calculus: Early Transcendentals 