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Subject: "Expectation of a function"     Previous Topic | Next Topic
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Conferences The CTK Exchange College math Topic #607
Reading Topic #607
Jim
guest
Mar-05-07, 03:17 PM (EST)
 
"Expectation of a function"
 
   Hi,

I am looking at the following problem.

E< 1/(x^T A x) >

A is diagonal N*N
x is a column vector 1*N

x is zero mean unit norm Gaussian vector.


Is this problem solvable?

It is easy if there is no inverse.


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mr_homm
Member since May-22-05
Mar-05-07, 07:29 AM (EST)
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1. "RE: Expectation of a function"
In response to message #0
 
   Let's start with a much simpler problem. If N=1 and A is the identity, the problem reduces to <1/x^2>. For x distributed like N(0,1), the integrand in the calculation of <1/x^2> will diverge like 1/x^2 near x=0, since the Gaussian distribution approaches a constant value there. Since this is a divergent integral, the expectation itself must diverge.

Since the problem has not solution in this simple case it'seems very unlikely that it could have a solution for N>1. If the signs of the diagonal elements of A are not all the same, then some cancellation would normally be possible, but as each individual term in the sum diverges, the cancellation is meaningless.

Hope this helps!

--Stuart Anderson


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