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I am given the parameters for a bivariate normal distribution ($\mu_x, \mu_y, \sigma_x, \sigma_y,$ and $\rho$). How would I go about finding the Var($Y|X=x$)? I was able to find E[$Y|X=x$] by writing $X$ and $Y$ in terms of two standard normal variables and finding the expectation in such a manner. I am unsure how to do this for the variance.

Also, how do I find the probability that both $X$ and $Y$ exceed their mean values (i.e., $P(X>\mu_x, Y > \mu_y)$)?

Thanks for the help!

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    what did you get for $\mathbb E[Y|X=x]$ ?2011-04-20
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    Well I was given numbers where mew x and mew y are 2 and negative 1 respectively. Variance of X is 4, variance of y is 1, and rho is negative root 3. I then expressed X as X = 2Z1+ 2 and Y as -root3/2*Z1 + 1/2*Z2 - 1 where Z1 and Z2 are standard normals and found E[Y|X=x] to be - root 3 / 2 * (x-2)/2 - 1.2011-04-20
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    You said $\rho$ is $-\sqrt 3$? That's impossible.2011-04-20
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    My bad its -(root3)/2.2011-04-20
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    I got $\mathbb E[Y|X=x]=-\frac{\sqrt 3}4(x-2)+1$ not $-1$.2011-04-20
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    I must have made an arithmetic mistake then! So now how do I go about finding Var(Y|X=x)?2011-04-20
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    I used a different approach. I'll type it up as a solution. I don't know how to continue with your approach.2011-04-20
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    Thank you. Much appreciated!2011-04-20
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    Sorry, you are right. Your $\mu_x=-1$ and I misread $1$.2011-04-20

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