# Normal distribution- cheak for mean and variance

• Jan 31st 2009, 04:12 AM
1234567
Normal distribution- cheak for mean and variance
Hi i was just wondering if the following was correct

Attachment 9921

Given X and Y, Z has the mean and Variance

Mean: 15

Variance:25
• Jan 31st 2009, 12:37 PM
mr fantastic
Quote:

Originally Posted by 1234567
Hi i was just wondering if the following was correct

Attachment 9921

Given X and Y, Z has the mean and Variance

Mean: 15

Variance:25

Look fine. Why would you doubt it?
• Feb 2nd 2009, 04:23 AM
anon18
can i ask how you got the mean and variance for Z
• Feb 2nd 2009, 04:50 AM
mr fantastic
Quote:

Originally Posted by anon18
can i ask how you got the mean and variance for Z

From standard theorems:

E(Z) = E(X - 4Y + 1) = E(X) - 4 E(Y) + 1.

Var(Z) = Var(X - 4Y + 1) = Var(X) + 4^2 Var(Y)
• Feb 2nd 2009, 04:55 AM
anon18
thanks...so how would you work out the correlation between X and Z and between Y and Z.
using correlation(X,Z)=cov(X,Z)/sqrt[var(x)var(Z)]

how would you work out the cov(X,Z)