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

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 18SE Chapter 2

Statistics for Engineers and Scientists | 4th Edition

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

Statistics for Engineers and Scientists | 4th Edition

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Problem 18SE

Let X and Y be random variables with μX = 1, σX = 2, μY = 3, σY = 1, and ρX,Y = 0.5. Find the means and variances of the following quantities.

a. X + Y

b. X - Y

c. 3X + 2Y

d. 5Y - 2X

Step-by-Step Solution:

Answer :

Step 1 of 1 :

Given,

let X and Y be independent random variables with  = 1,  =2, = 3, = 1 and

= 0.5

cov(X,Y) = () (  )

               =  (0.5) (2)(1)

              = 1

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

X + YX - Y3X + 2Y5Y - 2X

Step 2 of 5 :

a)

The claim is to find the Mean and Variance for Quantity X + Y

                              Where, = +

                                Here, = 1 and  = 3

               Therefore, = 1 + 3

                                        = 4

                      And   =   + + 2Cov(X,Y)

                  Where, = 2 and = 1

                         = 4 + 1 + 2(1)

                                     = 7

For the Quantity X + Y mean is 4 and variance is 7.

Step 3 of 5 :

b)

The claim is to find the Mean and Variance for Quantity X - Y

                              Where, = -

                                Here, = 1 and  = 3

               Therefore, = 1 - 3

                                        = -2

                      And   =   + - 2Cov(X,Y)

                  Where, = 2 and = 1

                         = 4 + 1 - 2(1)

                                     = 3

For the Quantity X - Y mean is -2 and variance is 3.

Step 4 of 5

Chapter 2, Problem 18SE is Solved
Step 5 of 5

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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