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Unformatted text preview: lecture 9, Review, Probability and Discrete Random Variables Probability Discrete rv lecture 9, Review, Probability and Discrete Random Variables Probability Probability • Probabilities are numbers used to measure the chance or likelihood that particular events occur. Probabilities can be based on experimental results (relative frequency method) or on logic (classical method); in some cases also on past experiences /knowledge /expertise (subjective probabilities). • Probabilities are between zero and one, inclusive. • Statistical tools: Venn diagrams, formulas for unions and intersections, complementation rule, addition rule, multiplication rule. • Concepts of conditional, independent and mutually exclusive events • A tree diagram can be helpful in illustrating and analyzing the sample space. Probabilities sometimes can be summarized and calculated more easily using a contingency table (e.g., Exercises 3.11, 3.343.37). lecture 9, Review, Probability and Discrete Random Variables Probability Discrete rv lecture 9, Review, Probability and Discrete Random Variables Probability Exercise 3.20  3.21 John and Jane are married. The probability that John watches a certain television show is 0.4. The probability that Jane watches the show is 0.5. The probability that John watches the show, given that Jane does, is 0.7. a. Find the probability that both John and Jane watch the show. b. Find the probability that Jane watches the show, given that John does. c. Do John and Jane watch the show independent of each other? Justify your answer. d. Find the probability that either John or Jane watches the show. lecture 9, Review, Probability and Discrete Random Variables Probability Discrete rv lecture 9, Review, Probability and Discrete Random Variables Probability Exercise 3.20  3.21, ctd a. P ( John ∩ Jane ) = P ( Jane ) P ( John  Jane ) = . 5 * . 7 = . 35 b. P ( Jane  John ) = P ( John ∩ Jane ) P ( John ) = . 35 . 4 = . 875 . c. No. P ( Jane  John ) 6 = P ( Jane ) . d. P ( John )+ P ( Jane ) P ( John ∩ Jane ) =0.4+0.50.35=0.55 lecture 9, Review, Probability and Discrete Random Variables Probability Discrete rv lecture 9, Review, Probability and Discrete Random Variables Probability Exercise 3.20  3.21, ctd Alternatively, using a contingency table: Jane watches Jane doesn’t watch John watches 0.5*0.7=0.35 0.4 John doesn’t watch Total 0. 5 1 ⇒ Jane watches Jane doesn’t watch John watches 0.35 0.05 0.4 John doesn’t watch 0.6 Total 0. 5 0. 5 1 ⇒ Jane watches Jane doesn’t watch John watches 0.35 0.05 0.4 John doesn’t watch 0.15 0.45 0.6 Total 0. 5 0. 5 1 ⇒ answers lecture 9, Review, Probability and Discrete Random Variables Probability Discrete rv lecture 9, Review, Probability and Discrete Random Variables Probability Simpson’s Paradox Sex Bias in Graduate Admissions • University of California, Berkeley • 44% of male applicants and 35% of female applicants were admitted — Gender bias?...
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 Fall '09
 AnthonyChan
 Standard Deviation, Variance, Probability theory, John ∩ Jane

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