2.9.1 Poisson

Question 1

what is the poisson distribution used to model?

Answer 1

The Poisson distribution is a discrete distribution used to model the occurrences of an event during
a fixed interval, where the occurrences in disjoint intervals are independent. The interval is usually
“time”, but it can be other quantities

Question 2

what is the pmf of the poisson distribution?

Answer 2

p(x) = (e^-λ))(λ)^x)/(x!)

Question 3

what is the mean and variance of the poisson distribution?

Answer 3

λ

Question 4

what does λ represent?

Answer 4

λ is the average rate at which events occur in a fixed interval of time or space. It represents the expected number of occurrences in that interval.

Question 5

what distribution is the sum of poisson r.v.s?

Answer 5

also poisson

Question 6

In a poisson the number of events in one interval is ____ of the numverof events in a nonoverlapping interval

Answer 6

independent