Derivation of a joint occupancy distribution via a bivariate inclusion and exclusion formula
Tóm tắt
Consider a supply of balls randomly distributed into n distinguishable urns and assume that the number
of balls distributed into any specific urn is a random variable with probability function
. The joint probability function and binomial moments of the number K
i
of urns occupied by i balls each and the number K
j
of urns occupied by j balls each, i≠j, given that a total of S
n
=m balls are distributed into the n urns, are derived in terms of convolutions of q
x
, x=0,1, . . . and their finite differences. Also, some illustrating examples are discussed.