Poisson distribution: P(X = k)
For rare events with a known average rate λ; the k! in the denominator is easily forgotten.
Worked example
On average 3.0 support requests arrive per hour (Poisson). What is P(exactly 2 requests in an hour)?
Worked solution
- 1.P(X = k) = e^(−λ) · λ^k / k!
- 2.= e^(−3.0) · 3.0^2 / 2! = 0.2240
Typical mistake: Forgetting k! in the denominator.
Your turn
Three problems of exactly this type, each time with new numbers. Comma or point; fractions like 1/6 work too.
Task 1 of 3Poisson distribution
Task
On average 4.0 support requests arrive per hour (Poisson). What is P(exactly 3 requests in an hour)?
P(X = 3) (4 decimal places)
Comma or point; fractions like 1/6 work too.
Formulas for this topic
- P(X = k) = e^(−λ) · λᵏ / k!
- E(X) = Var(X) = λ
- P(X ≥ 1) = 1 − e^(−λ)
Typical mistake: Forgetting k! in the denominator.
Frequently asked questions
What is the typical mistake in "Poisson distribution: P(X = k)"?
Forgetting k! in the denominator.
When do I use Poisson instead of binomial?
For many trials with a very small probability, or when only the average rate λ is known.