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Re: MultinormalDistribution Question

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  Re: MultinormalDistribution Question Tomas Garza <tgarza10@msn.com> - 2011-07-11 11:00 +0000

#3658 — Re: MultinormalDistribution Question

I know about "joint" pdf - don't know about "combined" pdf. Now, if it's 
the joint pdf we're talking about, what you want -I guess - is the mean and standard deviation of the "conditional" pdf, given that x = 6.3.
(BTW, there are a number of errors in your data, which I corrected as follows:
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]
also, try not to use capitalized names for your variables).

In that case, the mean is given by the following integral:
In[8]:= NIntegrate[y pdf/.x->6.3, {y,-Infinity, Infinity}]/PDF[MarginalDistribution[dist,1], 6.3]
Out[8]= 5.6
and I leave the variance for you to calculate.

-Tomas

> Date: Sun, 10 Jul 2011 05:01:17 -0400
> From: s123@epix.net
> Subject: MultinormalDistribution Question
> To: mathgroup@smc.vnet.net
>
> 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*sig=
ma2}
> 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
>
>
>
>

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