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CTK Exchange
Jim
guest
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Mar-05-07, 03:17 PM (EST) |
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"Expectation of a function"
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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
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Mar-05-07, 07:29 AM (EST) |
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1. "RE: Expectation of a function"
In response to message #0
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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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