The Galton board, despite being used as a pedagogical illustration, actually violates the independence and identical distribution assumptions because a ball's trajectory and peg interactions are highly dependent and non-uniform across pegs.

factualpending

Speaker

Unidentified Speaker — But what is the Central Limit Theorem? [zeJD6dqJ5lo]

Evidence Quote

Is it the case that the way a ball bounces off of one of the pegs is independent from how it's going to bounce off the next peg? Absolutely not... is it the case that the distribution of possible outcomes off of each peg are the same for each peg that it hits? Again, almost certainly not

Source

But what is the Central Limit Theorem?3Blue1Brown
Created: 8/10/2026, 3:51:19 PM

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