# conditional probability with bivariate normal dist. help

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• November 21st 2009, 07:56 AM
Intsecxtanx
conditional probability with bivariate normal dist. help
Assume that X and Y have a bivariate normal distribution with parameters $\mu_{X} = 14, \sigma^2_{X} = 4^{2}, \mu_{Y} = -1, \sigma^2_Y = 3^2, \rho = 0.9$

$(a) P (0 < Y \le 1)$

$(b) P (0 < Y \le 1 | X = 18)$

Thanks for your help!
• November 21st 2009, 02:53 PM
matheagle
You left out the mean of Y.
The first part is basic, the second you need to know the conditional distribution of Y given X.
You can find that after....
'In the bivariate case the conditional distribution of Y given X is'
in http://en.wikipedia.org/wiki/Multiva...l_distribution
Then perform the usual standardization to use the N(0,1) table.
• November 21st 2009, 08:09 PM
Intsecxtanx
Yes, I just realized. Thank you for your help!