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# Lecture10 - ECO 220Y Lecture 10 Probability Migiwa Tanaka...

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ECO 220Y Lecture 10 robability Probability Migiwa Tanaka Reading : 6.1,6.2,6.3 1

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Outline troduction Introduction Intersection and Union Joint, Marginal Union, and Conditional Probabilities dependence Independence Probability Rules Complement Rule Multiplication Rule Addition Rule robability Tree Probability Tree 2
Probability Link between population and sample l i Sampling POPULATION SAMPLE (parameters) X (statistics) Inference In most cases, only sample (a part of population) is available for statistical analysis. Since population parameters are unknown to us, we have to 3 deal with uncertainty. ECO220Y

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Random Experiments andom Experiment: A random process of producing Random Experiment: outcomes xample1: oll d ie obta in an outcome 12345 or 6 Example1: Roll a die, obtain an outcome, 1,2,3,4,5 or 6. Example2: Flip a coin, obtain an outcome, head or tail. Example3: Roll a die for 10 times and obtain mean. Is collecting a sample and computing the sample mean a random experiment? p 4
Sample Space mple space (S): Sample space (S): Exhaustive: List all possible outcomes t l l E l i Ot b l ( l )   k O O O S ,..., , 2 1 Mutually Exclusive: Outcome can be only one (no overlap) Probability of each outcome must be between 0 and 1 & t 1 they sum up to 1. Event: Any collection of outcomes of an experiment. Example: Toss a coin twice Sample Space: S={(HH), (HT), (TH),(TT)} Event that head appears once: {(HT) ,(TH)}. Event that tail appears at least once: {(HT) ,(TH), (TT)} We are interested in finding probability of a particular event. 5

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Intersection and Union tersection: Two ents both ccurs Intersection: Two events both occurs Denote “A and B” or “A ת B.” l F t k f d d d Example: From a stack of cards, draw a card. event A: draw a heart t B A B event B: draw a queen Drawing heart queen is intersection of event A and event B.
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Lecture10 - ECO 220Y Lecture 10 Probability Migiwa Tanaka...

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