 A closely related concept is the Lexis variation.Let "k" samples each of size "n" be drawn at random.Let the probability of success ("p") be constant and let the actual probability of success in the "k"th sample be "p"1, "p"2, ... , "p"k. 

The average probability of success ("p") is 

The variance in the number of successes is

where var( "p"i ) is the variance of the "p"i.