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Unformatted text preview: Stat C180 / C236 Homework 1 key J. Sanchez UCLA Department of Statistics Instructions (1) Homework must be typed and answered in the order given (problem 1(a)(b)(c)(d) first, problem 2(a)(b)... second, etc...) (2) Undergrads and grads will answer all questions. (3) Include in each part of the homework only the answer. R code and R output (without mistakes), must be included in the appendix to the question. For example, for question 1.a, write only the answer and your comments. The code and output for that part of the question will be in the appendix (the last part of question 1). (4) No late homework under any circumstances. (5) Write your name and ID this way: Last name, first name, UCLA ID, date, Homework number. (6) Do not just give a number as an answer. For example, if asked for probability that posterior proportion is larger than 0.7, write Prob ( p > . 7) = . 3, say and write comments or explanations if needed. (7) The homework must be turned in in lecture (no mail box, no e-mail). Problem 1. Marginal and conditional probability (Ho ff chapter 2, exercise 2.1) : The social mobility data from Section 2.5 (Ho ff ) gives a joint probability distribution on ( Y 1 , Y 2 ) = (fathers occupation, sons occupation). Using this joint distribution, calculate the following distributions: Figure 1: Table shown on Ho ff chapter 2 section 2.5 (a) the marginal probability distribution of a fathers occupation; b) the marginal probability distribution of a sons occupation; Marginal for fathers occupation Fathers occupation Probability Farm 0.11 Operatives 0.279 Craftsmen 0.277 Sales 0.099 Professional 0.235 height Marginal for sons occupation Sons occupation Probability Farm 0.023 Operatives 0.26 Craftsmen 0.24 Sales 0.125 Professional 0.352 Sept 23, 2010 (Revised October 4, 2010) 1 Stat C180 / C236 Homework 1 key J. Sanchez UCLA Department of Statistics (b) the conditional distribution of a sons occupation, given that the father is a farmer; P(sons occupation | father = farmer) Sons occupation P(sons occ | father = farmer) Farm P(son farmer | father farmer) = 0.018 / 0.11 = 0.163 Operatives P(son Operative | father farmer) = 0.035 / 0.11 = 0.318 Craftsmen P(son craftsman | father farmer) = 0.031 / 0.11 = 0.281 Sales P( son Salesman | father farmer) = 0.008 / 0.11 = 0.072 Professional P(son professional | father farmer) = 0.018 / 0.11 = 0.163 (c) the conditional distribution of a fathers occupation, given that the son is a farmer. P(father occupation | son = farmer) Fathers occupation P(Fathers occ | son = farmer) Farm P(father farmer | son farmer) = 0.018 / 0.023 = 0.782 Operatives P(father Operative | son farmer) = 0.002 / 0.023 = 0.086 Craftsmen P(father craftsman | son farmer) = 0.001 / 0.023 = 0.043 Sales P( father Salesman | son farmer) = 0.001 / 0.023 = 0.043 Professional P(father professional | son farmer) = 0.001 / 0.023 = 0.043 Problem 2. Urns (Ho ff chapter 2, exercise 2.5) : Suppose urn H is filled with 40% green balls and 60% red balls,...
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- Spring '10