2.22 (Continuation of Exercise 2.4.) A species of wasp lays its eggs on larvae.

Suppose that any larva has X encounters with wasps where X has the Poisson distribution, pr(X = k) = e−λλk k! , for k = 0, 1, 2,....

Suppose that an egg is always laid at the first encounter, but that at all subsequent encounters, single eggs are laid independently with probability

δ < 1 at each encounter. If pr denotes the probability that a larva receives r eggs, (r = 1, 2,...) then pr = δr−1(δ − 1)−re−λδ∞

i=r

λi

(δ − 1)i i!