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brain buster problem
Posted:
Jul 17, 1996 5:53 PM


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 15 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.... *************************************************************************** Robert Strawderman, Sc.D. Email: strawder@umich.edu Department of Biostatistics Office: (313) 936  1002 University of Michigan Fax: (313) 763  2215 1420 Washington Heights Ann Arbor, MI 481092029 Web: http://www.sph.umich.edu/~strawder/ ***************************************************************************



