Probability slides
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Title
Adding up randomness
Rolling dice
Counting heads
Not just coins
The right scaling
de Moivre–Laplace
Proof I: Stirling
Proof II: local limit
Proof III: Riemann sums
The CLT
Characteristic functions
The Gaussian's transform
Lévy's continuity theorem
Proof I: Taylor
Proof II: the limit
Watching it converge
Galton board
How fast?
When it fails
Summary
References: sources
References: further reading