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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 14RE
Textbook Problem
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Finding Expected Value, Variance, and Standard Deviation In Exercises 13–16, find the expected value, variance, and standard deviation for the given probability distribution.

x 1 2 3 4 5
P(x) 1 8 1 8 2 8 3 8 1 8

To determine

To calculate: The expected value, variance and standard deviation of the probability distribution:

x

1

2

3

4

5

P(x)

18

18

28

38

18

Explanation of Solution

Given Information:

The probability distribution:

x

1

2

3

4

5

P(x)

18

18

28

38

18

Formula used:

If a discrete random variable takes the values {x1,x2,,xm}, then the expected value of the random variable is defined as,

E(x)=x1P(x1)+x2P(x2)++xmP(xm)

Variance of the random variable is defined as,

V(x)=(x1μ)2P(x1)+(x2μ)2P(x2)++(xmμ)2P(xm)

The standard deviation of the random variable is defined as,

σ=V(x)

Calculation:

Consider the provided probability distribution.

x

1

2

3

4

5

P(x)

18

18

28

38

18

First use the provided probability distribution and the expected value formula E(x)=x1P(x1)+x2P(x2)++xmP(xm) to calculate the expected value of the probability distribution. So, the expected value is calculated as,

E(x)=(1)(18)+(2)(18)+(3)(28)+(4)(38)+(5)(18)=1+2+6+12+58=268=134

Thus, the expected value is E(x)=134

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Chapter 9 Solutions

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