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Lect9_L6_L7_handout1

Lect9_L6_L7_handout1 - lecture 9 Review Probability and...

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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, 3.34-3.37).
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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.
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lecture 9, Review, Probability and Discrete Random Variables Probability Discrete rv lecture 9, Review, Probability and Discrete Random Variables Probability
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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.
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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? Comparison is made over the whole university. Why not look at each individual department, which are smaller and more homogeneous groups.
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lecture 9, Review, Probability and Discrete Random Variables Probability Discrete rv lecture 9, Review, Probability and Discrete Random Variables Probability Simpson’s Paradox, ctd Men Women Number of Percent Number of Percent Major applicants admitted applicants admitted A 825 62% 108 83% B 560 63% 25 68% C 325 37% 593 34% D 417 33% 375 35% E 191 28% 393
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