"ZHANG Yan" <[EMAIL PROTECTED]> wrote in message
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
easily: P(Y1+Y2+...+YM = n)=\PRODUCT_{i=1..m} P(Xi=x_i) | \SUM_{i=1..m} x_i
= n?
or in words: multiply the chances that Xi equals a certain value as long as
the sum of all these values add up to the required n.
It kinda looks nice in discrete problems but becomes kind of a bore with
real numbers (it will be an (M-1)-fold integral)...
good luck
Martin
.
.
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