"ZHANG Yan" <[EMAIL PROTECTED]> wrote in
news:[EMAIL PROTECTED]:
> Hi, all, I'd like to ask a probability question.
>
> If the distribution of two independent random variable X1,X2 are
> given, i.e. P(X1), P(X2) are known, then I can understand that
>
> P(X1+X2=n)=\sum_{i=1}^{n} P(X1=i)P(X2=n-i)
>
> can we generalize this case, I mean,
>
> if the distributions of M indepednet random variables Y1,Y2,...YM are
> given, how to compute the following probability?
>
> P(Y1+Y2+...+YM = n)=?
>
> Thanks and Regards.
>
> --
> ZHANG Yan
>
>
I'm assuming from context that your variables are discrete with
nonnegative support (and that n is nonnegative). Compute the set P of
all order M partitions of n. An order M partition of n is an M-tuple of
nonnegative integers that sum to n. I'm not sure whether partitions are
generally written as tuples (ordered) or sets (unordered), but here we
need them ordered, meaning that for M = 3 and n = 5 the partition <1, 4,
0> is distinct from the partition <0, 1, 4>. Having found P, compute
the sum for all <y_1,...,y_M> in P of the products P(Y_1 = y_1)*...*P(Y_M
= y_M).
-- Paul
*************************************************************************
Paul A. Rubin Phone: (517) 432-3509
Department of Management Fax: (517) 432-1111
The Eli Broad Graduate School of Management E-mail: [EMAIL PROTECTED]
Michigan State University http://www.msu.edu/~rubin/
East Lansing, MI 48824-1122 (USA)
*************************************************************************
Mathematicians are like Frenchmen: whenever you say something to them,
they translate it into their own language, and at once it is something
entirely different. J. W. v. GOETHE
.
.
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