central limit theorem and normal distribution ee3060 probability yi-wen liu november 2010
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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