Lecture 3:Binomial and Poisson distribution

In this lecture we focus on the following points:

1. What is the characteristics of a Poisson distribution?

2. What is the probability distribution function, expectation and variance of Poisson distribution?

What is the characteristics of a Poisson distribution?

• The rate of occurance is constant throughout the given time interval or given space.
• The event happens singly and randomly and it is rare event.
• The probability of two events happening at the same time is negligible.
• The events happening in different time intervals or space are independent.

Examples of Poisson distribution includes no. of defects, demand of a certain item, no. of telephone calls etc.

What is the probability distribution function, expectation and variance of Poisson distribution?

• The p.d.f. of Poisson distribution is \[P(X=r)=\frac{e^{-\lambda}\lambda^{r}}{r!}\] where r=0,1,2,3,... (up to infinity)
• Expectation and variance: \[E(X)=\lambda\] \[Var(X)=\lambda\]

You can attempt Q1 - 3 in the tutorial 14B.