Throw N balls at random into B boxes. Let a be the average number of balls, N/B,in a box. Let P(x) be the probability that a given box has exactly x balls in it.(a) Show thatP(x) ≈axe−ax!.Certain assumptions are needed for this expression to be valid. What arethey?(b) Show that if a is large, the above Poisson distribution essentially becomes aGaussian distribution,P(x) = axe−ax!≈e−(x−a)2/2a√2πa

Swag , 10 Years ago

Grade 11