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Chapter2_print - STAT511 — Summer 2009 Lecture Notes 1...

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Unformatted text preview: STAT511 — Summer 2009 Lecture Notes 1 Chapter 2: Events and Laws of Probability June 17, 2009 2 Probability Chapter Overview This chapter focuses on “Probability” • Random Experiments, Sample Space and Events. – Random Experiment (R.E.) – Sample Space – Events – Examples • Introduction to Probability – Axiom – Properties – Examples • Counting Techniques – Combinations – Permutations • Conditional Probability – Definition – Related rules and theorem • Independence 2.1 Random Experiment, Sample Space & Events Random Experiment, Sample Space & Events • Random Experiment (R.E.) A R.E. is any action or process whose outcome is subject to uncertainty; i.e. many outcomes, each has a certain chance to happen. • Sample Space of a R.E. Denoted S , is the set of all possible outcomes of the R.E. • Event of a R.E. Denoted with capital letters (event A , B , E 1 , E 2 , etc), an event is any collection (subset) of outcomes contained in the sample space S of the R.E. – An event is said to be simple if it contains of exactly one outcome. – An event is said to be compound if it contains more than one outcome. Purdue University Chapter2˙print.tex; Last Modified: June 17, 2009 (W. Sharabati) STAT511 — Summer 2009 Lecture Notes 2 R.E. Example 2.1.1 Example 1 (Roll a Die) . What is the sample space? Outcomes: Landing 1, 2, 3, 4, 5, 6 face up. Sample Space: S = { 1 , 2 , 3 , 4 , 5 , 6 } . Events: Let E 1 be the event of getting a 2, then E 1 = { 2 } (simple event). Let E 2 be the event of getting a number greater than 3, then E 2 = { 4 , 5 , 6 } (compound event). Exercise 1. Let E 3 be the event of rolling a seven on a single die, what is E 3 ? 2. Let E 4 be the event of rolling an even number on a die, what is E 4 ? Example 2 (2.1.2 Tossing a Coin) . Toss a fair coin until a head appears, what is the sample space? Sample Space: S = { H, TH, TTH, TTTH, TTTTH, ···} . Events: 1. Let A be the event of tossing exactly 2 tosses, then A = { TH } . (simple event) 2. Let B be the event of tossing less than 4 tosses, then B = { H, TH, TTH } (compound event). 3. Let C be the event of tossing ≥ 2 and ≤ 5 tosses, then C = { TH, TTH, TTTH, TTTTH } (compound event). 4. Let D be the event of tossing more than 3 tosses, then D = { TTTH, TTTTH, TTTTTH, ···} (compound event). Relations From Set Theory An event is a set of outcomes, we may use set theory to form new events . • Union A ∪ B : is the event containing all outcomes in A or B . • Intersection A ∩ B : is the event containing all outcomes in both A and B . • Compliment A c : is the event containing all outcomes in the sample space S that are not contained in A . A ∪ A c = S • Mutually Exclusive (Disjoint) : A and B are said to be mutually exclusive if they contain no outcome in common....
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This note was uploaded on 03/30/2011 for the course STAT 511 taught by Professor Bud during the Spring '08 term at Purdue.

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Chapter2_print - STAT511 — Summer 2009 Lecture Notes 1...

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