Probability and Statistics Lecture 14

Continued

Probability and Statistics Lecture 13 Prerequsites

• Poisson’s Distribution

Poisson's Distribution

Poisson Distribution

This distribution is a limiting case of binomial distribution. Under the following assumptions.

• The number of trials $n$ tends to $\infty$.
• The probability of trial $p$ tends to $0$
• $\lambda =n\times p=finite$ Random Variable follows Poisson’s distribution with parameter $\lambda$ if it assumes the non negative integral values and its probability distribution is given by

$$P(X=x)=\frac{e^{-\lambda }{\lambda }^x}{x!}$$

Note

$XP(\lambda )$ The expected / average / mean of the Poissons distribution is lambda

References

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• date: 2025.03.22
• time: 17:02

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References

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• date: 2025.02.12
• time: 14:09

Continued

Probability and Statistics Lecture 15