Re: MultinormalDistribution Question

*To*: mathgroup at smc.vnet.net*Subject*: [mg120169] Re: MultinormalDistribution Question*From*: Barrie Stokes <Barrie.Stokes at newcastle.edu.au>*Date*: Mon, 11 Jul 2011 06:57:09 -0400 (EDT)*References*: <201107100901.FAA24634@smc.vnet.net>

Hi Steve The following will give you some ideas (note that I haveI have repaired your CapSigma). mean1 = 5.8; sigma1 = 0.2; mean2 = 5.3; sigma2 = 0.2; rho = 0.6; mu = {mean1, mean2} CapSigma = {{sigma1^2, rho*sigma1*sigma2} , {rho*sigma1*sigma2, sigma1^2}} dist = MultinormalDistribution[mu, CapSigma] pdf = PDF[dist, {x, y}] plot1 = Plot3D[pdf, {x, 4, 7}, {y, 4, 7}, PlotRange -> All] pdfConditional = (PDF[dist, {x, y}] /. {x -> 6.3})/ Integrate[ PDF[dist, {x, y}] /. {x -> 6.3}, {y, 4, 7} ] // Simplify plotConditional = Plot[pdfConditional, {y, 4, 7}, PlotRange -> All] meanConditional = Integrate[ y pdfConditional, {y, 4, 7} ] sdConditional = Sqrt[ Integrate[ (y - meanConditional)^2 pdfConditional, {y, 4, 7} ]] Cheers Barrie >>> On 10/07/2011 at 7:01 pm, in message <201107100901.FAA24634 at smc.vnet.net>, Steve <s123 at epix.net> 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>