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# Lecture3standard - Statistics 511 Statistical Methods Dr...

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Statistics 511: Statistical Methods Dr. Levine Purdue University Fall 2011 Lecture 1: Introduction to Probability. Sample spaces, events, probability axioms Devore: Section 2.1-2.2 Aug, 2011 Page 1

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Statistics 511: Statistical Methods Dr. Levine Purdue University Fall 2011 Sample Space The sample space of an experiment S is the set of all its possible outcomes. Example: tossing the coin once we have the space S = { H,T } Example: tossing the coin twice and recording the outcomes produces S = { HH,HT,TH,TT } Example: roll a die with 6 faces and record the outcome. Then, S = { 1 , 2 , 3 , 4 , 5 , 6 } . Aug, 2011 Page 2
Statistics 511: Statistical Methods Dr. Levine Purdue University Fall 2011 Simple and Compound Events An event is a collection (subset) of outcomes contained in the sample subspace. It is simple if it consists of exactly one outcome and compound otherwise. Example: consider recording the freeway exit ( L or R ) for each of the 3 vehicles at the end of the exit ramp. The eight possible outcomes form the sample space S = { LLL,RLL,LRL,LLR,LRR,RLR,RRL,RRR } . Examples of simple events would be: E 1 = LLL E 2 = LRL Aug, 2011 Page 3

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Statistics 511: Statistical Methods Dr. Levine Purdue University Fall 2011 Examples of Compound Events Examples of compound events would be: Exactly one vehicle turns left A = { LRR,RLR,RRL } All three vehicles turn in the same direction B = { LLL,RRR } Aug, 2011 Page 4
Statistics 511: Statistical Methods Dr. Levine Purdue University Fall 2011 Some Relations from Set Theory The union of two events

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Lecture3standard - Statistics 511 Statistical Methods Dr...

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