Scheme of work: Year 12 Further Mathematics A-Level: Further Statistics 1: The Poisson Distribution
Throughout this unit, students learn to understand the Poisson distribution as a probability model and use it to solve real-life problems. Later, they use the Poisson distribution to approximate the binomial distribution as learning progresses.
E(X)=\sum_{x=0}^{\infty}{xP\left(X=x\right)=\lambda}Var(X)=\sum_{x=0}^{\infty}{x^2P(X=x)-\lambda^2=\lambda}
Students learn to use the Poisson distribution to model real-world problems.
Later, as learning progresses, they move from using the probability mass function to the Poisson PD function on the Casio classwiz calculator.
Students learn how to calculate probabilities of real-life models using the Poisson Distribution.
Later, as learning progresses use they adjust their Poisson model for different scenarios.
Students learn how to combine independent Poisson distributions.
Later, as learning progresses, they solve a range of problems involving linear combinations of independent Poisson distributions.
Students learn how to work out the mean and variance of a Poisson distribution.
Later, as learning progresses, they find the mean and variance of distributions to use the Poisson distribution as a model .
Students learn how to work out the mean and variance of a Binomial distribution.
Later, as learning progresses they use the mean and variance to calculate the probability and number of trials.
In this lesson, students explore the conditions under which the Poisson distribution can be used to approximate the Binomial distribution when n is large and p is small.
Later in the lesson, students will evaluate the accuracy of this approximation by calculating the percentage error between the two distributions. This allows them to critically assess when and why the Poisson model is appropriate.
Students learn how to carry out hypothesis tests to test for the mean of a Poisson distribution.
Later, as learning progresses students move from one- to two-tail tests at varying levels of significance.
Students learn how to find critical regions of a Poisson distribution using tables.
Later, as learning progresses students move from one- to two-tail tests at varying levels of significance.
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