   # 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 4 ( 3 − x ) , [ 0 , 4 ] ### 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 27RE
Textbook Problem
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## 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 4 ( 3 − x ) ,        [ 0 , 4 ]

To determine

To graph: The function using a graphing utility and determine whether the function f(x)=14(3x) represents a probability density function over the interval [0,4].

### Explanation of Solution

Given Information:

The function f(x)=14(3x) over the interval [0,4].

Graph:

Consider the provided function f(x)=14(3x).

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 14(3x).

Step 3: Press the [window] key and adjust the scale.

Xmin=0.5Xmax=2Xscl=0.25

And,

Ymin=0Ymax=4Yscl=1

Step 4: Press the [graph] key.

The bar graph of the function f(x)=14(3x) is obtained as,

Consider the provided function f(x)=14(3x) over the interval [0,4]

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