pakisagutan.. di ko to lam eh.. hehe!!

Poisson and Gaussian
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 that

P(x) ¼ is approximately equal to [(a^x)(e^-a)]/x!

Certain assumptions are needed for this expression to be valid. What are
they?

(b) Show that if a is large, the above Poisson distribution essentially becomes a
Gaussian distribution,

P(x) = [(a^x)(e^-a)]/x! and is approxiamtely equal to {e^[-(x-a)^2]/2a}/sq.rt. of [2a(pi)]