The Poisson distribution: scaling, equations and approximations
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 5 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- Random events, steady rate
- The Poisson model
- Scaling the mean
Read the transcript of the teaching part
Random events, steady rate
Cars at a junction, emails in an inbox, typing errors in a magazine. Each happens at random, one at a time, at some steady average rate. Count how many happen in a fixed interval and you have a Poisson distribution. It has one number, lambda, and almost every question is about getting the right lambda.
The Poisson model
X follows Po of lambda when events occur singly, at random, independently of each other, at a constant average rate. The probability of exactly r events is e to the minus lambda, times lambda to the r, over r factorial. The mean and the variance are both lambda. This is the signature of a Poisson distribution.
Scaling the mean
The rate is given for one interval. If you are asked about a different length of time, scale lambda to match. Cars arrive at 3.2 per minute. For a 3 minute period, lambda is 9.6. Write the new distribution before you calculate: X is Po of 9.6.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Normal approximation to Poisson · Poisson approximation to binomial.
The whole chapter: The Poisson Distribution.
Chapter 6.1: The Poisson distribution
- The Poisson distribution: scaling, equations and approximations 6 min
Also for A Level Maths 9709 Paper 6
Which topics come up most in A Level Maths 9709 Paper 6 past papers, counted from every paper since 2004.