joint pmf and covariance questions

macduff · #1 $Old$ November 2nd, 2009, 07:08 PM

I hope I have put this in the right section, technically I am doing this at uni but its pretty easy but for some reason I just don't know how to do it...
Anyway, I am having a bit of trouble using tables to find covariance and variance. This question is just an example I am stuck on from a previous exam where:

I don't really understand how to find: C(X,Y), Var(X), Var(Y) or C(X+3Y-1,X-2Y). The formula I have confuse me even more. Any help would be greatly appreciated.

statmajor · #2 $Old$ November 4th, 2009, 02:29 PM

$Cov(X,Y) = E(XY) - E(X)E(Y)$

$E(X) = \Sigma X_i P(X_i)$

$E(X^2) = \Sigma X^2_i P(X_i)$

$Var(X) = E(X^2) - E(X)^2$

Same idea with E(Y),Var(Y), and E(XY).

By the way, what is the formula you have?