Central Limit Theorem and Normal Distribution EE3060 Probability Yi-Wen Liu November 2010

Binomial approximated by normal distributions N=25 N=50 N=100

Binomial, now approximated by normal distributions N=25 N=50 N=100

Binomial, now approximated by normal distributions N=25 N=50 N=100

Review: Binomial(40,p) with Poisson Approximation

Conclusions Recall that binomial(N,p) is an independent sum of N Bernoulli r.v.’s N ↑, Central Limit Theorem applicable, Gaussian fits better and better –True for all p –Useful because, for large N, N! cannot be calculated by Matlab double-precision floating point