   Chapter 9.2, Problem 3E ### 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
1 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 ) = 3 4 x ( 2 − x ) , [ 0 , 2 ]

To determine

To prove: The function, f(x)=34x(2x) is a probability density function over the interval [0,2]

Explanation

Given Information:

The function, f(x)=34x(2x) over the interval [0,2]

Formula used:

Consider 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

Proof:

Consider the function,

f(x)=34x(2x)=34(2xx2)=34(2x)34(x2)

f(x) is the difference of a linear and a quadratic function.

Thus, f(x) is non-negative and continuous over the interval [0,2]

Now, evaluate abf(x)dx as,

02f(x)dx=3402(2x)dx3402(x2)dx=34202

### 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

#### Sketch the graphs of the equations in Exercises 512. xy=4

Finite Mathematics and Applied Calculus (MindTap Course List)

#### In Exercises 69-74, rationalize the numerator. 72. 2x3y3

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

#### 356dx= a) 2 b) 8 c) 6 d) 12

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

#### Rewritten as an iterated integral in polar coordinates,

Study Guide for Stewart's Multivariable Calculus, 8th 