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Sp05_EC41 - EC 41 UCLA Fall 2008 Sample Problems#5 RE...

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EC 41 UCLA Fall 2008 – Sample Problems #5; RE Section 4.5 and Ch 5 material Midterm 2 will cover material from Chapter 2, sections 2.4, 2.5, & 2.6 and Chapters 4 and 5 These problems will NOT be collected or graded, but they will be useful for studying for exams. - The following table is for a sample of 500 patients at a particular health maintenance organization (HMO). - Use it for questions 1 & 2 Smoker Non-Smoker Total: Have Heart Disease: 50 40 90 Do Not Have Heart Disease: 100 310 410 Total: 150 350 500 Event Probability 1) a) Form a partition of the four categories to the right. Smoker and disease = P(S D) = - select an individual at random from the population Smoker and no disease = P(S D ) = C of patients. Report the probability for each of the four Non-smoker and disease = P(S D) = C possibilities. Non-smoker and no disease = P(S D ) = C C b) It is impossible for an individual to be in two or more categories, thus the events are: disjoint or independent 2) a) Select an individual at random from the population of 500 patients. What is the probability they are i) a smoker; ii) non-smoker? Note, these two “events” also form a “partition of the sample space.” What is the sum of the two probabilities? b) Select an individual at random from the population of 500 patients. What is the probability they are i) have heart disease; ii) do not have heart disease? c) What it the probability of heart disease for a randomly chosen: i) Smoker, ii) Non-smoker d) What it the probability an individual is a smoker for a randomly chosen person: i) With Disease; ii) Without Disease e) Is the probability the a randomly chosen individual (from the population of 500) is both a smoker and has heart disease equal to the probability of a smoker times probability of heart disease? Is it true that: P(S D) = P(S)P(D)? f) Verify Bayes’ rule: ) ( ) | ( ) ( ) | ( ) ( ) | ( ) | ( C C D P D S P D P D S P D P D S P S D P + = 3) Consider two events, A and B. P(A) =.10; P(B|A) =.80; P(B|A C ) =.30 a) Probability of the complement of A: P(A C ) = b) Probability of A given B: P(A|B) = c) Unconditional probability of B: P(B) = 4) a) Consider two events, C and D which are disjoint What is the probability they both occur= P(C and D) = P(C D)? What is the probability that C occurs given that D occurred = P(C|D)? b) Consider two events, E and F which are independent If P(E) = .3 and P(F) = .2, what is the probability they both occur= P(E and F) = P(E F)? What is the probability that E occurs given that F occurred = P(E|F)? 5) At a particular school 10% of male students wear crew-cut haircuts. X = the number of students with crew-cuts in a random sample of 100 males.
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