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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 8 e − x / 8 , [ 0 , 8 ]

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
Publisher: Cengage Learning
ISBN: 9781305860919

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Section
BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
Publisher: Cengage Learning
ISBN: 9781305860919
Chapter 9, Problem 29RE
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 8 e x / 8 ,        [ 0 , 8 ]

To determine

To graph: The function using a graphing utility and determine whether the function f(x)=18ex/8 represents a probability density function over the interval [0,8].

Explanation of Solution

Given Information:

The function f(x)=18ex/8 over the interval [0,8].

Graph:

Consider the provided function f(x)=18ex/8.

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=18ex/8.

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

Xmin=0Xmax=8Xscl=1

And,

Ymin=0Ymax=0.25Yscl=0.01

Step 4: Press the [graph] key.

The graph of the function f(x)=18ex/8 is obtained as,

Consider the provided function f(x)=18ex/8 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

For x=8 in the interval [0,8], the function is evaluated as,

f(8)=18e8/8=18e1=0.367980.046

The function f is continuous and nonnegative for all values on the interval [0,8].

Since, 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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Chapter 9 Solutions

Calculus: An Applied Approach (MindTap Course List)
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