1. Consider the probability that every bin receives exactly one ball when n balls are
thrown randomly into n bins.
(a) Give the Poisson approximation of this probability, as determined by the proba-
bility distribution of the suitable Poisson random variable.
Hint: No derivation is needed, just give the probability that approximates.
(b) Determine the exact probability of this even
(c) Show that these two probabilities dier by a multiplicative factor that equals theprobability that
the Poisson random variable with parameter n takes on n asvalue.
(d) Explain why the fact stated in (c)
Solution
http://inst.eecs.berkeley.edu/~cs174/fa10/sol4.pdf
go to second page you will find your answer