Seeing Theory - Chapter 3: Probability Distributions (Central Limit Theorem)
by Daniel Kunin · Brown University
Interactive browser simulations where you pick a source distribution, set the sample size, and watch sample means pile up into a normal curve in real time. Makes the sample-size dependence of the CLT something you manipulate rather than read.
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Where Durrett gives one canonical proof, Tao gives three - characteristic functions, the moment method, and the Lindeberg exchange - and explains what each buys you. That comparative view is what turns the CLT from a memorised theorem into a technique you can transfer. Six sets of graduate lecture notes with exercises, building from measure-theoretic foundations to Notes 3 on the weak and strong laws, Notes 4 on the central limit theorem, and Notes 5 on variants including Berry-Esseen and stable laws.