Lecture 3 Poisson Distribution

What is poisson distribution

Discrete distribution which models occurrences over space or time.

• we get x number of successes over a given time or space

• x must be a non negative and whole integer (1,2,3,4…)

• The number of successes is proportional to the length of time or space

• eg number of buses at bus stop in 1 hour or no of accidents on 200km road

Poisson relation to binomial

• used when P is very small and n is very large

• is an approximation of binomial distribution

Poisson probability function

Note that the mean myoo is the only parameter for poisson, so the mean and variance equal each other.

Poisson and binomial threshold and when to combine means

When P is small and n is very large.

When nP ≤ 7.

so if we then have to use poisson, we compute the mean as nP and carry on as usual using the poisson function.