Apologies in advance for cross-posting.
For integers 1 <= k <= m let b1, ..., bk be a random sample without
replacement from { 1, 2, ..., m }.
I am interested in the expectation of the product of b1 through bk,
E( b1 * b2 * ... * bk ) = E .
Some study reveals that
E = c0 + c1 m + ... + ck m**k ,
but correct and explicit expressions for most of the coefficients
( c0, ... ck ) in terms of k are elusive (e.g., it is easy to show that
ck = 2 ** ( - k ), but the others are harder).
Does anybody know, or know where to find, correct and explicit expressions
for ( c0, ... c(k-1) ) in terms of k, or some other explicit expression for
E valid for all k and m?
There is a reward of a statistics book of your choice, not to exceed 50
British pounds (US$75) in price (including shipping), for the first person
who sends, by email or fax, either the correct explicit expressions or a
correct literature reference to them.
Many thanks and best wishes, David
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Professor David Draper
Head of Statistics Group web http://www.bath.ac.uk/~masdd
Department of email [log in to unmask]
Mathematical Sciences phone UK (01225) 826 222, nonUK +44 1225 826 222
University of Bath fax UK (01225) 826 492, nonUK +44 1225 826 492
Claverton Down
Bath BA2 7AY England
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