Conditional expectations of bivariate normal distributions

Ryuuzakie
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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.
 
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how about the joint denisty function?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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