According to Peter Shirely paper, one pdf(probability density function) can be defined for the union of the light sources and pick only one using a random number from this density:

p(x) = a1 * P1(x) + (1-a1) * P2(x);

This has been referred to as mixture densities. where a=[0,1] and P1 is a pdf for selecting a point on the L1 geometry(usually 1/A). If the random number is less than a1 then the total estimate is (estimated L1)/a1.

This has been extended for N: p(x) = a1 * P1(x) + a2 * P2(x) + ... + an * Pn(x)

My question is how one pick two or multiple light sources, instead of just one, from the above density and what the estimate would be in that case.