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Statistics / Statistics for Engineers and Scientists 4 / Chapter 2 / Problem 18SE

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Let X and Y be random variables with ?X = 1, ?X = 2, ?Y =

Chapter 2, Problem 18SE

(choose chapter or problem)

QUESTION:

Let X and Y be random variables with $\mu_X=1$, $\sigma_X=2$, $\mu_X=3$, $\sigma_Y=1$, and $\rho_{X,Y}=0.5$. Find the means and variances of the following quantities.

a. $X+Y$

b. $X−Y$

c. $3X+2Y$

d. $5Y−2X$

Equation Transcription:

${\mu{}}_{X}=1$

${\sigma{}}_{X}=2$

${\mu{}}_{Y}=3$

${\sigma{}}_{Y}=1$

${\rho{}}_{X,Y}=0.5$

$X+Y$

$X−Y$

$3X+2Y$

$5Y−2X$

Text Transcription:

mu_X=1

sigma_X=2

mu_Y=3

sigma_Y=1

rho_{X,Y}=0.5

X+Y

X−Y

3X+2Y

5Y−2X

Questions & Answers

QUESTION:

Let X and Y be random variables with $\mu_X=1$, $\sigma_X=2$, $\mu_X=3$, $\sigma_Y=1$, and $\rho_{X,Y}=0.5$. Find the means and variances of the following quantities.

a. $X+Y$

b. $X−Y$

c. $3X+2Y$

d. $5Y−2X$

Equation Transcription:

${\mu{}}_{X}=1$

${\sigma{}}_{X}=2$

${\mu{}}_{Y}=3$

${\sigma{}}_{Y}=1$

${\rho{}}_{X,Y}=0.5$

$X+Y$

$X−Y$

$3X+2Y$

$5Y−2X$

Text Transcription:

mu_X=1

sigma_X=2

mu_Y=3

sigma_Y=1

rho_{X,Y}=0.5

X+Y

X−Y

3X+2Y

5Y−2X

ANSWER:

Answer :

Step 1 of 1 :

Given,

let X and Y be independent random variables with ${\mu{}}_{X}$ = 1, ${\sigma{}}_{X}$ =2, ${\mu{}}_{Y}$ = 3, ${\sigma{}}_{Y}$ = 1 and

${\rho{}}_{X,Y}$ = 0.5

cov(X,Y) = ( ${\rho{}}_{X,Y}$ ) ( ${\sigma{}}_{X}$ ${\sigma{}}_{Y}$ )

= (0.5) (2)(1)

= 1

The claim is to find the mean and variances for the following quantities

X + Y

X - Y

3X + 2Y

5Y - 2X

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Solution Found!

Let X and Y be random variables with ?X = 1, ?X = 2, ?Y =

Questions & Answers

Study Tools You Might Need

Chapter: 12 Problem: 11P

Chapter: 4 Problem: 4.27

Chapter: 5 Problem: 11P

Chapter: 6 Problem: 6.4-3

Chapter: 19 Problem: 2

Chapter: 21 Problem: 2

Chapter: 8 Problem: 36

Chapter: 9 Problem: 1

Not The Solution You Need? Search for Your Answer Here:

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