# Thread: Normal distribution- cheak for mean and variance

1. ## Normal distribution- cheak for mean and variance

Hi i was just wondering if the following was correct

Given X and Y, Z has the mean and Variance

Mean: 15

Variance:25

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

Given X and Y, Z has the mean and Variance

Mean: 15

Variance:25
Look fine. Why would you doubt it?

3. can i ask how you got the mean and variance for Z

4. 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)

5. 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)