You can express this as a double integral...
or let ....
so . Thus
is just or
NOW is a normal with mean zero and ...(you get the variance, but that's not needed)
So P(W>0)=.5
Hello all i am having trouble breaking down this question. Anyone can help is much appreciated:
Let X = (X,Y) and is N(0, "summation sign") with "summation sign" :
| 1 p |
| p 1 |
Write an integral expression for P(X "subset sign" D) where D is a set on the plane. Evaulate it for D = {(x,y) : x <= y} by using the theorem:
If X is a multivariate Normal N (u, "summation sign") then aX is (au, a"summation sign"a"transpose sign")
Im not too sure about the theorem bit which i stated above cause there might have been a typo in the book.
Incase it is too vague there are hints given that says:
The whole idea is to Transform X and Y into standard normal variables (the formula for Z which is used to look up in the normal distribution table) so it can be used to find out the the probability of P(X,Y <= 0).
oh and u is the mean ie the "mean sign"
Thank you!!