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5.3 Poisson Distribution:
Poisson distribution was discovered by the French mathematician and physicist Simeon Denis Poisson who published it in 1837. Poisson distribution is a limiting case of the binomial distribution under the following conditions.
(i) n, the number of trials is indefinitely large, i.e., nà ∞.
(ii) p, the constant probability of success for each trial is indefinitely small, i.e., pà 0.
(iii) np = λ, is finite. Thus p = λ/n, q = 1-λ/n, where λ is a positive real number.
A random variable X is said to follow a Poisson distribution if it assumes only non-negative values and its probability mass function is given by
Here λ is known as the parameter of the distribution.
We shall use the notation X~ P(λ) to denote that X is a Poisson variate with parameter λ.
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