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)=α1P1(x)+(1−α1)P2(x)
This has been referred to as mixture densities. where α1∈[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 α1 then the total estimate is (estimated L1)/α1.
This has been extended for N: p(x)=α1P1(x)+α2P2(x)+⋯+αnPn(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.