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...
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?
Last edited by Dason; 11-21-2010 at 04:39 PM. Reason: Merged 4 posts into 1
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