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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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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 9 x ( 3 x ) , [ 0 , 3 ]

To determine

To calculate: Whether the function, f(x)=29x(3x) is a probability density function over the interval [0,3] or not

Explanation

Given Information:

The function f(x)=29x(3x) over the interval [0,3].

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)=29x(3x)

f(x) is continuous over the interval [0,3].

f(x) is negative in the intervals (,0) and (3,) and is positive in the interval [0,3] as shown below:

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

Step1: Open Ti-83.

Step2: Press Y= button.

Step3: Write the equation as Y1=(2/9)X(3X).

Step4: Press Enter button.

Step5: Press Window and set is as:

Xmin=6;            Xmax=8;             Xscal=1Ymin=8;            Ymax=2;             Yscal=1

Step6: Press Graph button.

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