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# Let X and Y be random variables with ?X = 1, ?X = 2, ?Y = ISBN: 9780073401331 38

## Solution for problem 18SE Chapter 2

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:

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

Step 5 of 5

##### ISBN: 9780073401331

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