# Thread: sum of normal distribution help

1. ## sum of normal distribution help

X~N(3,5) Y~N(-7,2)
What is the distribution of Z=4X-Y/3 ?

is it just

=- Y/3 + 4X
=- Y~N(-7/3,2/3) + X~N(-7/3 + 3,2/3 + 5)
= X~N(-7/3 + 3,2/3 + 5) - Y~N(-7/3,2/3)

?

What is the covariance of X and Z?

I don't understand how to do this...

2. ## Re: sum of normal distribution help

Again you need several basic properties:

1. If are independent normal random variables,
then is also normally distributed.

2. If is a normal random variable,
then is also normally distributed.

3.

4.

5. If are independent,
then

6.

3. oh right, i forgot to mention that X, and Y are independent.

i'm not understanding how to multiply normal distributions by constants,
is 4*X~N(3,5) = X~N(12,20) ?

EDIT: i now get Z~N(43/3, 20.011) is this right?

and i think i figured out the covariance

Cov(X,Z)=Coz(X,4X-1/3*Y)
=Coz(X+0Y,4X-1/3*Y)
=4Cov(X,X)-1/3 Cov(X,Y)
=4Var(X)-1/3(0) <--- by independence
=4Var(X)
=4*5
=20

Is this right?

 Tweet

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts