"ZHANG Yan" <[EMAIL PROTECTED]> wrote: > if the distributions of n indepednet random variables Y1,Y2,...Yn > are given, ie. P(Yi=yi) is known for i=1..n; > > I need to find the following probability: > P(Y1+Y2+...+Yn = M)=?
The density for the sum of independent variables is the convolution of the density of each variable. This applies to both continuous and discrete variables. That is, if you have density functions p1, p2, ..., pn, then the density of the sum is p1 * p2 * ... * pn, denoting the convolution with the asterisk. The convolution is more quickly calculated by appealing to the relation FT(f*g) = FT(f) FT(g), that is, the Fourier transform of the convolution is the product of the Fourier transforms. This is generally much, much faster than computing the convolution via summation or integration. I use Octave (http://www.octave.org) for calculations of this kind. For what it's worth, Robert Dodier -- ``If you could count for a year, would you get to infinity, Or somewhere in that vicinity?'' -- Tom Lehrer . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
