Poisson distribution

• Poisson distribution

 

A discrete probability distribution. It gives the probability of an event happening a certain number of times (k) within a given interval of time or space, meaning that it gives the probability of a discrete(i.e., countable) outcome.

---

---

$\mathrm{\lambda <!--\; \lambda \; -->}=kp$

then

$p=\frac{\mathrm{\lambda <!--\; \lambda \; -->}}{k}$

---

- X : A random variable following a Poisson distribution

- k : The number of times an event occurs

- P(X = k) : The probability that an event will occur k times

- e : Euler’s constant (approximately 2.718)

- λ : The average number of times an event occurs

- ! : The factorial function

---

Example.

 

- Defective probability : One out of every 500 items at the factory, 1/500.

- X : The number of defective items out of 1,500 products

 

1) Binomial Distribution

 

 

2) Poisson distribution

 

λ = xp = 1500 X 1/500 = 3

 

 

https://www.scribbr.com/statistics/poisson-distribution/

https://pmxsg.tistory.com/111

https://angeloyeo.github.io/2021/04/26/Poisson_distribution.html