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Topic: brain buster problem
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 Robert L Strawderman Posts: 9 Registered: 12/18/04
brain buster problem
Posted: Jul 17, 1996 5:53 PM
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Here's a tough problem -- any ideas?

Is it possible to construct a (dependent) sequence of rv's
{t_i, i=1..n} such that for all i,j,k=1..n

1. E[t_i] = 0

2. E[t^2_i] = 1

3. E[t_i t_j] = 0 i!=j

4. E[t_i t_j t_k] = 0 i!=j!=k

5. E[t^2_i t_j] = 0 i < j

6. E[t^2_i t_j] = 1 i >= j

Generating a sequence of rv's which satisfies 1-5 is rather
trivial - its 6 that appears to be the killer. Note that for 6
to be satisfied, its sufficient if E[t^2_i | t_j] = t^2_j and
E[t^3_j]=1. However, constructing such a sequence seems difficult
if one wishes to preserve 3.

The t_i's can be discrete, continuous, or a mix.
Any ideas would be appreciated....

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Robert Strawderman, Sc.D. Email: strawder@umich.edu
Department of Biostatistics Office: (313) 936 - 1002
University of Michigan Fax: (313) 763 - 2215
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Ann Arbor, MI 48109-2029 Web: http://www.sph.umich.edu/~strawder/
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