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Unformatted text preview: 1 CHAPTER 6: PROBABILITY Stats & Prob. for Bus. Mgmt (Stat1100) Jochem b Overall Goals b 1. Getting familiar with basic probability theory so that we can compute probabilities of events. s Chance of winning the lottery? Having 3 out of 5 correct? 2 Probability Theory s If IQ scores are normally distributed, what’s the probability that someone will have an IQ above 130? s If trucks crossing a bridge follow a Poisson distribution, what’s the prob. of 5 trucks crossing in the next 10 min? b 2. Understanding discrete and continuous probability distributions that are underlying inference estimation. Probability Theory b Road map: Chap 68 b Chapter 6: Probability s Random Experiments , Events, Sample Space s Joint, marginal & conditional probabilities 3 s Probability Operators & Rules s Trees, Bayes’s Law & Counting b Chapter 7: Discrete Probability Distributions s Random Variables; Bivariate, Binomial & Poisson distribution b Chapter 8: Continuous Probability Distributions s Uniform, Normal, Exponential distribution s Student’s t , ChiSquared, Fdistribution Thereafter, chapter 9 on sampling distributions makes the transition towards estimation and inference. Probability b Chapter 6: Overview b 1. Basic Terminology of Probability Theory b 2. Joint, Marginal and Conditional Probability . Probability Operators & Rules 4 b 3. Probability Operators & Rules b 4. Trees & Bayes’s Law b 5. Counting b 6. Exercises b 1.1 Random Experiment b A random experiment is any process that leads to one or several basic outcomes (or a list thereof).* b Examples: 5 Probability s 1. Flipping coins s 2. PA Lottery “Treasury Hunt” s 3. Writing an exam s 4. Playing football s 5. Batting baseballs * Basic outcomes need to be mutually exclusive. (If we consider the weather as a random experiment, then for example “sunny” and “rainy” could not be basic outcomes as both can occur simultaneously.) An experiment is called “random ” if its result cannot be predicted with certainty. b 1.2 Sample Space b The sample space of a random experiment is the list of all possible basic outcomes : 6 Probability b Examples: s 1. Flipping coins { Heads, Tails } s 2. PA Lottery “Treasure Hunt” { (1,2,3,4,5), …(26,27,28,2930) } s 3. Writing an exam { 0,1,2, … ,125 points} s 4. Football scores { …, (24:14), … } s 5. Batting averages { …, 0.25, …, 0.39, … } countable uncountable b 1.3 Probability b Chance b Critical component of statistical inference. sed extensively in decision aking under uncertainty. 7 Probability b Used extensively in decisionmaking under uncertainty. b 1.3 Probability b A probability is the chance of one (or more) specific outcome(s) of the sample space occurring....
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 Spring '08
 Chiappetta
 Conditional Probability, Probability, Probability theory, Pittsburgh, Probability space

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