   # 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 ### 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 14RE
Textbook Problem
1 views

## 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

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Find more solutions based on key concepts
A population of N = 7 scores has a mean of = 13. What is the value of X for this population?

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Baby Boomers and Social Security Benefits Aging baby boomers will put a strain on Social Security benefits unle...

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Given: mABD=2x+5 mDBC=3x4 mABC=86 Find: mDBC

Elementary Geometry For College Students, 7e

Find each product: (ab+2)(ab2)

Elementary Technical Mathematics

True or False: If converges and converges, then converges.

Study Guide for Stewart's Multivariable Calculus, 8th

If y = f (g(x)) then y′ = f′(g′(x)).

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Perform each operation. a2+3-2a2-4

College Algebra (MindTap Course List)

Testing Exponential Data In Exercise S-8 through S-16, test the given data to see whether they are exponential....

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List) 