Revision as of 17:41, 23 September 2008 by Kdosenba (Talk)

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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

$ P(A|B) = \frac{P(A \cap B)}{P(B)} $

Propertie:

1) $ P(A|B) \ge 0} $ 2) $ P( \Omega |B) >= 0} $ 3) if A1 and A2 are disjoint

  $ P(A1 \cup A2|B) = P(A1|B) + P(A2|B)} $

Bayes rule and total probability

$ P(A|B) = \frac{P(A \cap B)}{P(B)} $

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

Alumni Liaison

Recent Math PhD now doing a post-doctorate at UC Riverside.

Kuei-Nuan Lin