Re: MultinormalDistribution Question

*To*: mathgroup at smc.vnet.net*Subject*: [mg120178] Re: MultinormalDistribution Question*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Mon, 11 Jul 2011 06:58:46 -0400 (EDT)*References*: <201107100901.FAA24634@smc.vnet.net>

First, your covariance matrix is not symmetric definite. I think you probably meant: CapSigma = {{sigma1^2, rho*sigma1*sigma2}, {rho*sigma1*sigma2, sigma2^2}} Assuming that, you can get the conditional expectation from the definition: Integrate[y PDF[dist, {6.3, y}], {y, -Infinity, Infinity}]/ PDF[MarginalDistribution[dist, 1], 6.3] 5.6 Alternatively, you can use Mathematica 8 built in NExpectation function: NExpectation[y \[Conditioned] 6.299 <= x <= 6.301, {x, y} \[Distributed] dist] 5.6 Once you have the conditional expectation, you can compute the conditional variance, e.g. Chop[Integrate[(y - 5.6)^2*PDF[dist, {6.3, y}], {y, -Infinity, Infinity}]/PDF[MarginalDistribution[dist, 1], 6.3]] 0.0256 Andrzej Kozlowski On 10 Jul 2011, at 11:01, Steve wrote: > Hello, > > Can someone help me with this ? > > I have 2 normal distributions; dist1 describes x and dist2 describes > y. Each are fully defined and are correlated to one another by the > correlation coefficient. How can I detemine the mean and standard > deviation of the expected normal distribution that is associated with > a given x value from dist1 ? > > An example: > mean1 = 5.8 > sigma1 =0 .2 > > mean2 = 5.3 > sigma2 = 0.2 > > Correlation Coefficient, rho = 0.6 > > Given an x value of 6.3 (from dist1) what is the corresponding mean > and standard deviation of y ? > > I can view the combined density function from the following: > > Mu = {mean1, mean2} > CapSigma = {{sigma1^2, rho*sigma1*sigma2} , {rho, rho*sigma1*sigma2} > dist = MultinormalDistribution[Mu,CapSigma] > pdf = PDF[dist,{x,y}] > plot1 = Plot3D[pdf, {x,4,7},{y,4,7}, PlotRange->All] > > but can't see how to determine the mean and the standard deviation of > y for a given value of x, like 6.3 > > Any help would be appreciated. > > Thanks, > > --Steve > > > >

**References**:**MultinormalDistribution Question***From:*Steve <s123@epix.net>