6.1 The Poisson distribution

5 of 5 objectives have lessons · 0 studied · 0 secure

Lessons

The Poisson distribution: calculating probabilitiesModel random events with the Poisson distribution and compute P(X = r) from the parameter lambda. 10 min, not started
Mean, variance and modelling random eventsFor X ~ Po(λ) the mean and variance are both λ, and the equality is what makes the Poisson model testable against real data. 10 min, not started
Poisson as an approximation, and the normal approximationWhen a binomial becomes a Poisson, and when a Poisson becomes normal - including the continuity correction. 10 min, not started

5 objectives

What Cambridge says you should be able to do, in our words. Codes are the topic number plus the objective’s position.

6.1.1

Use formulae to calculate probabilities for the distribution Po(λ).

Taught in: The Poisson distribution: calculating probabilities · 6 questions

6.1.2

Use the fact that if X ~ Po(λ) then the mean and the variance of X are each equal to λ.

Proofs are not required.

Taught in: Mean, variance and modelling random events · 4 questions

6.1.3

Understand the relevance of the Poisson distribution to the distribution of random events, and use the Poisson distribution as a model.

Taught in: Mean, variance and modelling random events · 4 questions

6.1.4

Use the Poisson distribution as an approximation to the binomial distribution where appropriate.

The conditions that n is large and p is small should be known: approximately n > 50 and np < 5.

Taught in: Poisson as an approximation, and the normal approximation · 3 questions

6.1.5

Use the normal distribution, with continuity correction, as an approximation to the Poisson distribution where appropriate.

The condition that λ is large should be known: approximately λ > 15.

Taught in: Poisson as an approximation, and the normal approximation · 4 questions