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MultinormalDistribution Question


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.



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