   # In Exercises 7–9, 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 16 , [ 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 7TYS
Textbook Problem
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## In Exercises 7–9, 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 16 ,   [ 0 , 8 ]

To determine

To graph: Whether the function f(x)=116 represents a probability density function over the interval [0,8] and graph the function using a graphing utility.

### Explanation of Solution

Graph:

Consider the provided function f(x)=116.

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=1/16.

Step 3: Press the WINDOW key and adjust the scale.

Xmin=0Xmax=8Xscl=1

And,

Ymin=0Ymax=516Yscl=0.1

Step4: Press Enter button.

Step5: Press the Graph key.

The graph of the function is obtained as,

Consider the provided function f(x)=116 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

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

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