Poisson distribution

Question 1

How is a Poissonly distributed variable notated?

Answer 1

X∼Po(λ), where λ is the expected number of occurrences in a given interval

Question 2

For a random variable X∼Po(λ), how can P(X=x) be calculated?

Answer 2

e^(-λ)*λˣ/x!

Question 3

For a random variable X∼Po(λ), how can E(X) be calculated?

Answer 3

λ

Question 4

For a random variable X∼Po(λ), how can Var(X) be calculated?

Answer 4

λ

Question 5

What conditions are required for a Poisson distribution?

Answer 5

• 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

Question 6

If the number of events per unit time is ∼Po(λ), how is the number of events per n unit times distributed?

Answer 6

∼Po(nλ)

Question 7

When and how can a random variable X∼B(n,p) be approximated by a Poisson distribution?

Answer 7

When n is large and p is small, then X≈∼Po(np)