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Probability & Distributions

Core probability technique + the distribution zoo.

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Bernoulli: the atom of probability
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Beta: probability of a probability (conjugate to Bernoulli)
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Coloring: when 2 colors aren't enough — escalate to ≥3
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Complement: when 'not the thing' is easier
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Conditional probability: shrinking the sample space
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Which distribution? — the decision tree
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Exponential: time between Poisson events; memoryless
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Extremal principle: lean on the most extreme element
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Geometric probability: probability as a ratio of areas
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Gumbel: the limiting distribution of the max
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Invariants: the quantity the move can't touch
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Normal: the CLT limit, the workhorse
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Parity: when a 2-coloring decides the question
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Pigeonhole: when collision is unavoidable
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Symmetry: when relabeling does the counting for you
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Geometric: trials until the first success
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recommend Bernoulli: the atom of probability first
Binomial: counting successes in n Bernoulli trials
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recommend Bernoulli: the atom of probability +1 more first
Bayes' rule: inverting the conditioning
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recommend Conditional probability: shrinking the sample space first
Law of total probability: average over the hidden case
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recommend Conditional probability: shrinking the sample space first
Gamma: sum of k independent Exponentials
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recommend Exponential: time between Poisson events; memoryless first
Weibull: extreme value type III; failure modeling
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recommend Exponential: time between Poisson events; memoryless first
Central Limit Theorem: turn a sum into a Normal
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recommend Variance of sums + law of total variance +2 more first
Lognormal: multiplicative Normal — stock prices
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recommend Normal: the CLT limit, the workhorse first
Negative Binomial: trials until the k-th success
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recommend Geometric: trials until the first success first
Lévy / stable: heavy-tailed, stable under sums
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recommend Central Limit Theorem: turn a sum into a Normal first