Tuesday, July 28, 2015

De-Moivre Laplace Theorem

In probability theory, the De-Moivre – Laplace theorem is a normal approximation to the Binomial distribution. It is a special case of the central limit theorem.
It states that the binomial distribution of the number of ‘successes’ in n independent Bernoulli trials with probability p success on each trial is approximately a normal distribution with mean np and sd, if n is very large & some conditions are satisfied. This theorem allows us to use areas under the normal curve to approximate binomial probabilities when n is sufficiently large.
That is the normal distribution with µ = np and σ2 = np(1-p) provides a very close approximation to the binomial distribution when n is large. In fact, the approximation is often adequate for p gets closer to 0 or 1.
Larger values of n are needed to obtain the same accuracy.

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