Re: MultinormalDistribution Question

*To*: mathgroup at smc.vnet.net*Subject*: [mg120179] Re: MultinormalDistribution Question*From*: Ray Koopman <koopman at sfu.ca>*Date*: Mon, 11 Jul 2011 06:58:57 -0400 (EDT)*References*: <ivbpsr$o5b$1@smc.vnet.net>

On Jul 10, 2:03 am, Steve <s... 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 The conditional mean of y given x is (x - mx)*r*sy/sx + my, and the conditional standard deviation is sy*Sqrt[1 - r^2], where mx & my are the marginal means, sx & sy are the marginal standard deviations, and r is the correlation.