16/3848–12FE Reference Handbook 10.6 · Engineering Probability and Statistics · p. 85 Poisson

Handbook formula

Poisson Probability Mass Function

Poisson counts on p. 85 are f(x;λ) = λ^x e^{−λ}/x!, with mean = variance = λ. The ratio P(x+1)/P(x) = λ/(x+1) follows from that mass function. It is not a separate printed recurrence.

Mean rate (events per interval)
Integer count 0,1,2,…
Probability of exactly x events

Step-by-step solved example

Defects arrive as Poisson with λ = 2 per shift. Find P(X = 0) and P(X = 1).

λ = 201234Replay
Poisson counts are a discrete cousin of the normal for large λ.
  1. 1. Zero events

    P(0) = e^{−2} ≈ 0.1353.

  2. 2. One event

    P(1) = e^{−2} · 2 / 1 = 2e^{−2} ≈ 0.2707.

Answer: P(0) ≈ 0.135, P(1) ≈ 0.271

10 practice questions

0/10 correct

1.For Poisson, E[X] equals

2.Var(X) for Poisson(λ) is

3.λ = 3, P(X=0) =

4.Binomial(n=100, p=0.02) is often approximated by Poisson with λ =

5.P(X=x+1)/P(X=x) equals

6.λ = 1, P(X=2) is nearest

7.A Poisson random variable is

8.If λ doubles, P(X=0)

9.Standard deviation of Poisson(λ=16) is

10.Sum of independent Poisson(λ1) and Poisson(λ2) is