S2- Poisson Distribution Flashcards
1
Q
What is the Poisson distribution defined as?
A
X~ Po(λ)
2
Q
Conditions for Poisson
A
Events happen independently of each other
Events happen singly in space or time
Events happen at a constant rate
3
Q
P(X = x)
A
(e^(-λ) x λ^x)/x!
4
Q
E(X)
A
λ
5
Q
Var(X)
A
λ
6
Q
What does λ represent?
A
The expected number of successes in a given amount of time
7
Q
When can the binomial distribution be approximated to the Poisson?
A
When n is large (usually >50) and p is small
8
Q
If X~B(n,p), what is the Poisson approximation?
A
Y~ Po(np)
9
Q
What is given in the probability tables for the Poisson?
A
P(X≤x) for λ between 0.5 and 10
10
Q
How do you work out P(X≥x)?
A
1-(P(X≤x-1))
