1
Q
How is a Poissonly distributed variable notated?
A
X∼Po(λ), where λ is the expected number of occurrences in a given interval
2
Q
For a random variable X∼Po(λ), how can P(X=x) be calculated?
A
e^(-λ)*λˣ/x!
3
Q
For a random variable X∼Po(λ), how can E(X) be calculated?
A
λ
4
Q
For a random variable X∼Po(λ), how can Var(X) be calculated?
A
λ
5
Q
What conditions are required for a Poisson distribution?
A
- The events occur singly in space or time
- The events are independent
- The events occur at a constant rate, such that the mean number of occurrences in the interval is proportional to the length of the interval
6
Q
If the number of events per unit time is ∼Po(λ), how is the number of events per n unit times distributed?
A
∼Po(nλ)
7
Q
When and how can a random variable X∼B(n,p) be approximated by a Poisson distribution?
A
When n is large and p is small, then X≈∼Po(np)
