The Poisson Distribution Flashcards
The Poisson distribution is used for events that:
- Occur randomly in space and time.
- occur singly (not simultaneously).
- occur independently (one doesn’t affect another).
- occur at a constant rate (the mean in a given time is proportional to the size of the interval)
The probability, where x is the numbers of trials and λ is the mean, is calculated?
e^-λ multiplied by λ^x / x!
For a Poisson distribution, the mean and variance are both what?
λ - they are equal
A binomial X~B(n,p) can be approximated to a poisson if?
n>50 and np<5
How to approximate a binomial X~B(n,p) to a poisson?
W~Po(np)
When approximating a binomial to a possion, what is better and more accurate?
The larger the n and the smaller the p
A poisson X~Po(λ) can be approximated to a normal if?
If λ > 15
How to approximate a poisson X~Po(λ) to a normal?
Y~N(λ,λ)
When a possion is approximated to a normal, what is a better and more accurate approximation?
The larger λ
When approximating a poisson to a normal, what must be applied?
A continuity correction of 1/2
Why do poisson and binomial need a continuity correction?
They are discrete
