   Chapter 9.2, Problem 11E ### 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 ) = 2 x − 3 2 , [ 0 , 3 ]

To determine

To calculate: Whether the function f(x)=2x32 is a probability density function over the interval [0,2] or not.

Explanation

Given Information:

The provided function f(x)=2x32 over the interval [0,2].

Formula used:

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

Calculation:

Consider the function,

f(x)=2x32

If f(x) is continuous over the interval [0,2] then the f(x) is negative in the interval (0,34):

Now use Ti-83 graphing calculator to draw the graph:

Step1: Open Ti-83.

Step2: Press Y= button.

Step3: Write the equation as Y1=2X3/2.

Step4: Press Enter button.

Step5: Press Window and set is as:

Xmin=3;            Xmax=3;             Xscal=0.5Ymin=3;            Ymax=3;             Yscal=0.5

Step6: Press Graph button.

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