I have two probability distributions p1(x) and p2(x) given by (x_1i, w_1i) and (x_2i, w_2i) respectively, i.e. they are both represented by sets of particles. I need to create the pdf p(x) = p1(x) . p2(x), their product. I read that for functions supported on integers (these would be like the delta functions of the particles), multiplying is the same as convolution. But I still can't figure out how to create a new pdf represented by (x_i, w_i) from these two sets. Can somebody give me some ideas?