   # Finding Expected Value, Variance, and Standard Deviation In Exercises 39-44, use the given probability density function over the indicated interval to find the (a) expected value, (b) variance, 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. f ( x ) = 1 7 , [ 0 , 7 ] ### Calculus: An Applied Approach (Min...

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

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
Publisher: Cengage Learning
ISBN: 9781305860919
Chapter 9, Problem 39RE
Textbook Problem
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## Finding Expected Value, Variance, and Standard Deviation In Exercises 39-44, use the given probability density function over the indicated interval to find the (a) expected value, (b) variance, 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. f ( x ) = 1 7 , [ 0 , 7 ]

(a)

To determine

To calculate: The expected value of probability density function f(x)=17 over the interval [0,7].

### Explanation of Solution

Given Information:

The probability density function is defined as

f(x)=17 over the interval [0,7].

Formula used:

For any probability density function f of a continuous random variable x over the interval [a,b], the expected value of x is defined as,

μ=E(x)=abxf(x) dx

The integration formula,

xndx=xn+1n+1+C

Where, n is any real number and C is a constant.

The Fundamental theorem,

abf(x) dx=F(b)F(a)

Calculation:

Consider the provided probability density function.

f(x)=17 over the interval [0,7].

Use the formula E(x)=abxf(x) dx for the provided probability density function to calculate the expected value

(b)

To determine

To calculate: The variance of probability density function f(x)=17 over the interval [0,7].

(c)

To determine

To calculate: The standard deviation of probability density function f(x)=17 over the interval [0,7].

(d)

To determine

To graph: The probability density function f(x)=17 over the interval [0,7].

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