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Sample Space, Axioms of probability (finite spaces, infinite spaces)

$ P(A) \geq 0 $ for all events A

Properties of Probability laws


Definition of conditional probability, and properties thereof


Bayes rule and total probability


Definitions of Independence and Conditional independence


Definition and basic concepts of random variables, PMFs


The common random variables: bernoulli, binomial, geometric, and how they come about in problems. ALSo their PMFs.

Geometric RV

P(X=k) = (1-p)^(k-1) * p for k>=1

$ E[X] = 1/p $


Definition of expectation and variance and their properties

$ Var(X) = E[X^2] - (E[X])^2 $


Joint PMFs of more than one random variable

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