Z = X - 2Y + 1
so
hi, I am preparing for a final in my least favorite class and could use a little help with this preparation problem.
Initially X and Y were normal with given mean and variance, and it asked for the distribution of the same Z = h(X,Y). I know that's a linear combination and was able to calculate the distribution no problem.
Now I am a little stuck on the next part,
Assume now that (X,Y) is a normal vector with covariance Cov(X,Y) = 4. What is the distribution of Z = X - 2Y + 1? Compute P( Z > 5).
I can get the second part if I am able to find the distribution of Z, which is where I get stumped.
Does the information in the beginning about the normal dist. of X, Y help? All I can see in my notes about this is
Cov(X,Y) = E(XY) - ux*uy where ux is the mean of x, same for y
thanks for any help at all!