Central Limit Theorem and Normal Distribution

EE3060 Probability

Yi-Wen LiuNovember 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