   Chapter 9.2, Problem 2E ### 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
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# 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 ) = 1 8 x , [ 0 , 4 ]

To determine

To prove: The function, f(x)=18x is a probability density function over the interval [0,4].

Explanation

Given Information:

The function, f(x)=18x over the interval [0,4].

Proof:

Consider the function, f(x)=18x.

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)=18x being the linear function is non-negative and continuous over the interval [0,4]

Now, evaluate abf(x)dx as,

041

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