Review of 120A - Review of PSTAT 120A Spring 2009...

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Review of PSTAT 120A Spring 2009 Probability Measure (Probability Function) – Given a sample space, S , a probability function, Pr[.], is a function satisfying the following three conditions: i) Non-negative : ii) Total probability of 1 : iii) Countable Additivity : Note : Pairwise mutually exclusive events means that Empty Set Complements Subsets Valid Probabilities Additive Rule Conditional Probability Multiplicative Rule Independence Bayes’ Theorem Random Variable (RV) A random variable is a mapping (function) from the sample space, S , to the real numbers, . Random variables are usually denoted by capital letters, X , and the possible values that they can take on are denoted by lower case letters, x . Example : If we are counting the number of accidents that occur on the 101, then X= the number of accidents that occur, and x =0, 1, 2, …
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Discrete Random Variable – A discrete random variable, X, is a mapping from the sample space, S , to the real numbers, , whose support is either finite or countably infinite.
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