ClassNotes-Chapter-04-v4-part-1

ClassNotes-Chapter-04-v4-part-1 - CHAPTER 4: PROBABILITY...

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1 © Sven Thommesen 2011 CHAPTER 4: PROBABILITY (v4 part 1) [Edited 09/23/08] [ Work In Progress ] TABLE OF CONTENTS PART 1 (This part covers sections 4.1-4.3 in the textbook) 1. BASIC CONCEPTS OF PROBABILITY 2. STATISTICAL EXPERIMENTS 3. THE PROBABILITY OF OUTCOMES: SIMPLE EXPERIMENTS 4. WHAT IF PROBABILITY IS NOT CLASSICAL? ASSIGNING PROBABILITY. A. CLASSICAL B. EMPIRICAL (RELATIVE FREQUENCY) C. EMPIRICAL (PROBABILITY FUNCTIONS) D. SUBJECTIVE 5. USING CLASSICAL PROBABILITY 6. SIMPLE EXPERIMENTS AND EVENTS OF INTEREST 7. THE PROBABILITY OF OUTCOMES: EXTENDED EXPERIMENTS A. REPEATED SIMPLE EXPERIMENTS B. COMPOUND EXPERIMENTS 8. EXTENDED EXPERIMENTS AND EVENTS OF INTEREST 9. WHAT IF EXPERIMENTS ARE NOT INDEPENDENT? A. IF ORDER MATTERS: PERMUTATIONS (SEQUENCES) B. IF ORDER DOES NOT MATTER: COMBINATIONS (GROUPS) C. COMMITTEE SELECTIONS [optional] 10. INDEPENDENT EXPERIMENTS AND GROUPS [optional]
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2 1. BASIC CONCEPTS OF PROBABILITY In the context of this course, the term “probability” refers to a mathematically precise way of talking about the notion of likelihood . In daily life we employ such phrases as “What are the chances that …?”, “What are the odds in favor of …?”, “What is the likelihood of X happening?”. The answers are usually fuzzy, approximate, and subjective. In some cases, however, it is possible to use mathematics to compute exact numbers for probabilities! EXAMPLES Some examples of the kinds of questions we will discuss in this and the next two chapters: If I flip a coin, what is my probability of getting Heads? If I roll a fair die, what is the probability of rolling a 4 or a 6? If I purchase one ticket in the Georgia state lottery, what is my probability of having the winning one? How many different tickets would I have to purchase to be sure to win? If I roll a die 5 times in a row, what is the probability I‟ll roll a sequence containing only 4‟s and 5‟s? If I draw 5 cards in a row from a normal deck, what is my probability of drawing the sequence 2, 3, 4, 5, 6 of Clubs? What is the probability that Hillary Clinton will be our next president? How about Ron Paul? How about your instructor? What is the probability that Auburn, Alabama will be hit by a Category 5 hurricane this year? What is the probability that exactly 7 people will enter the post office during the next hour? If people‟s heights are normally distributed with a mean of 5‟10‟‟ and a standard deviation of 4‟‟, what is the probability that a person randomly selected from the Auburn student body will be over 7‟ tall?
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3 FORMALIZING THINGS A BIT We will use the term probability to denote a numerical measure of likelihood , a measure that obeys certain rules: a) Let us use the notation P(x) or Pr(x) to mean “the probability that event x will happen.” b) P(x) ≥ 0 and P(x) ≤ 1: Our me asure of probability is a (real) number between 0.0 and 1.0, inclusive. Mathematicians combine the two rules and write them this way: 0.0 ≤ P(x) ≤ 1.0 .
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ClassNotes-Chapter-04-v4-part-1 - CHAPTER 4: PROBABILITY...

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