   Chapter 9.3, Problem 12E ### 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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# Finding Expected Value, Variance, and Standard Deviation In Exercises 1-12, use the given probability density function over the indicated interval to find the (a) expected value,(b) variance using the alternative formula, and(c) standard deviation of the random variable.(d) Then sketch the graph of the probability density function and locate the mean on the graph. See Examples 1, 2, and 5. f ( x ) = 1 18 9 − x , [ 0 , 9 ]

(a)

To determine

To calculate: The expected value for the probability density function, f(x)=1189x,[0,9].

Explanation

Given Information:

The provided probability density function is f(x)=1189x,[0,9].

Formula used:

The expected value for the continuous random variable, x with density function f(x) within the interval [a,b] is computed as:

μ=E(x)=abxf(x)dx

Calculation:

The expected value for the provided probability density function within the interval [0,9] can be calculated as:

μ=09(1189x)xdx=118

(b)

To determine

To calculate: The variance for the probability density function, f(x)=1189x,[0,9].

(c)

To determine

To calculate: The standard deviation for the probability density function, f(x)=1189x,[0,9].

(d)

To determine

To graph: The probability density function, f(x)=1189x,[0,9] and mark the mean value.

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