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Basic Probability Theory (I)

Basic Probability Theory (I)Intro to Bayesian Data Analysis & Cognitive ModelingAdrian Brasoveanu[partly based on slides by Sharon Goldwater & Frank Keller and John K. Kruschke]Fall 2012 UCSC Linguistics1 Sample Spaces and EventsSample SpacesEventsAxioms and Rules of Probability2 Joint, Conditional and Marginal ProbabilityJoint and Conditional ProbabilityMarginal Probability3 Bayes Theorem4 Independence and Conditional Independence5 Random Variables and DistributionsRandom VariablesDistributionsExpectationTermino logyTerminology for Probability Theory : experiment:process of observation or measurement; ,coin flip; outcome:result obtained through an experiment; , coinshows tails; sample space:set of all possible outcomes of anexperiment; , sample space for coin flip:S={H,T}.Sample spaces can be finite or : Finite Sample SpaceRoll two dice, each with numbers 1 6. Sample space:S1={ x,y :x {1,2,..,6} y {1,2,..,6}}Alternative sample space for this experiment sum of the dice:S2={x+y:x {1,2.}}

A manufacturer knows that the probability of an order being ready on time is 0.80, and the probability of an order being ready on time and being delivered on time is 0.72.

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