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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
