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Statistics – Central Limit Theorem, Probability Generating Functions and Quality of Test
infoWhy this? The central limit theorem explains why normal approximations can describe sample means under suitable conditions, while probability generating functions provide algebraic tools for analysing discrete distributions, their moments, and sums of independent random variables. Studying test quality through error probabilities and power helps us assess how effectively a test can detect a genuine effect.
scheduleWhy now? The distributions studied in Year 12 and earlier this term now provide a broad set of examples for generating functions and distributional approximations. Earlier hypothesis testing can be revisited through error probabilities and power, bringing the statistics strand together around the reliability of statistical methods.