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In Exercises 7–9, 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 ) = 3 − x 6 , [ − 1 , 1 ]

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Calculus: An Applied Approach (Min...

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

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BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
Publisher: Cengage Learning
ISBN: 9781305860919
Chapter 9, Problem 8TYS
Textbook Problem
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In Exercises 7–9, 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 ) = 3 x 6 , [ 1 , 1 ]

To determine

To graph: Whether the function f(x)=3x6 represents a probability density function over the interval [1,1] and graph the function using a graphing utility.

Explanation of Solution

Graph:

Consider the provided function f(x)=3x6.

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 (3X)/6.

Step 3: Press the WINDOW key and adjust the scale.

Xmin=1Xmax=1Xscl=0.5

And,

Ymin=0Ymax=0.9Yscl=0.1

Step 4: Press the GRAPH key.

The graph of the function is obtained as,

Consider the provided function f(x)=3x6 over the interval [1,1].

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=0 in the interval [1,1], the function is evaluated as,

f(0)=306=36=12

Now, show that abf(x) dx=1.

Evaluate the integral 113x6 dx. Use the formula xndx=xn+1n+1+c and integrate

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Chapter 9 Solutions

Calculus: An Applied Approach (MindTap Course List)
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