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Elementary probability front page
Bounding probabilities by expectations
Condition on the first thing that happens
To compute covariance, use bilinearity
To compute probabilities of unions and intersections, use the inclusion-exclusion formula
To compute the probability that exactly k of n events occur, use generalized inclusion-exclusion
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Littlewood-Paley heuristic for derivative
Geometric view of Hölder's inequality
Diagonal arguments
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Try to prove a stronger result
Use self-similarity to get a limit from an inferior or superior limit.
Prove a consequence first
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