Teaching probability generating functions (PGFs) in A-Level Further Mathematics can be challenging. From understanding the definition and key property GX(1) = 1 to exploring standard distributions like Binomial, Poisson, Geometric, and Negative Binomial, there’s a lot to cover.
My latest blog post features four concise video tutorials that help teachers deepen their subject knowledge while saving lesson planning time. The videos cover expected values, variances, sums of independent random variables, and transformations of discrete random variables—all with clear explanations and ready-to-use examples.
Check out the videos to boost your confidence in teaching PGFs and streamline your preparation.
Students learn how to create a PGF to describe a probability distribution.
Later, as learning progresses they use probability generating functions to find the probability of a range of events.
Students learn how to use the standard PGFs for discrete probability distributions.
Later, as learning progresses they prove the standard distribution formulae for Binomial, Poisson, and Geometric distributions from the first principals.
Students learn how to calculate the mean of a PGF.
Later, as learning progresses they use the differentiation chain and product rules to find the variance.
Students learn how to create a PGF to describe a probability distribution.
Later, as learning progresses they use probability generating functions to find the probability of a range of events.
Students learn how to create a probability generating function to describe a probability distribution.
Later, as learning progresses they use probability generating functions to find the probability of a range of events.
Students learn how to use the standard probability generating functions for discrete probability distributions.
Later, as learning progresses they prove the standard distribution formulae for Binomial, Poisson, and Geometric distributions from the first principals.
Students learn how to calculate the mean of a probability-generating function.
Later, as learning progresses they use the differentiation chain and product rules to find the variance.
Students learn how to use probability-generating functions to find the sum of independent random variables.
Later, as learning progresses they find the mean and variance of the resulting probability generating function.
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