Conditional expectations of bivariate normal distributions

[Ryuuzakie]

Hey guys, I'm having a bit of a problem with this question...

Homework Statement

If X and Y have a bivariate normal distribution with $$m_X=m_y=0$$ and $$\sigma_X=\sigma_Y=1$$, find:

a) E(X|Y=1) and Var(X|Y=1)
b) Pr(X+Y>0.5)

Homework Equations

N/A

The Attempt at a Solution

Apologies, but I don't seem to know where to start on this one.

 

[lanedance]

how about the joint denisty function?

 

[lanedance]

PS
http://mathworld.wolfram.com/BivariateNormalDistribution.html