   Chapter 9.2, Problem 9E ### 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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# Identifying Probability Density Functions In Exercises 7-12, 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. See Examples 1 and 2. f ( x ) = 1 7 e − x / 7 ,      [ 0 , 3 ]

To determine

To graph: The function, f(x)=17ex/7 and find the function represents is a probability density function over the interval [0,3] or not.

Explanation

Given Information:

The function, f(x)=17ex/7 over the interval [0,3].

Graph:

Use the ti-83 graphing calculator to plot the graph of the function.

Step 1: Press the [Y=] key, then there will appear the equations for y.

Step 2: Enter the equations Y1 as (1/7)e^(x/7).

Step 3: Set the window as shown below:

Xmin=50;Xmax=100;Xscl=50Ymin=0;Ymax=0.3;Yscl=0.1

Step 4: Press [GRAPH] button,

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

Consider the function,

f(x)=17ex/7

f(x) is non-negative and continuous over the interval [0,3]

Now, evaluate abf(x)dx as,

03f(x)dx=

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