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I'm using Mathematica to find a closed-form solution for a conditional expectation. The distribution I am interested in is a mixture of two trivariate normals. In particular, I would like to know the conditional expectation of one random variable conditional on the other two being held fixed at some vector {a,b}.

The code below sets up the expectation, but I can't make it run. I believe the problem is in the part where I specify the distribution, as the other part works fine when I try it with other distributions. Any help is much appreciated!

 muA = {muA1, muA2, muA3}
 covA = {{varA1, covA12, covA13}, {covA12, varA2, covA23}, {covA13, 
 covA23, varA3}}
 muB = {muB1, muB2, muB3}
 covB = {{varB1, covB12, covB13}, {covB12, varB2, covB23}, {covB13, 
 covB23, varB3}}

 Expectation[{x1} \[Conditioned] {x2, x3} == {"a", "b"}, {x1, x2, 
 x3} \[Distributed] 
 MixtureDistribution[{0.5, 0.5}, {MultinormalDistribution[muA, covA],
 MultinormalDistribution[muB, covB]}]]
jackblun
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  • Did you get an error or something? What did you mean with "but I can't make it run"? – Thargor Oct 15 '15 at 21:17
  • No error code. It just repeats the command I typed in as opposed to giving me the algebraic form of the expectation. Thanks for your patience with me, I'm new to Mathematica! – jackblun Oct 17 '15 at 12:50

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