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old exams - Ec 120A OLD EXAMS(Foster I DO NOT DISCUSS OLD...

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Ec 120A OLD EXAMS (Foster) I DO NOT DISCUSS OLD EXAMS! These are provided to you to give you some idea of the level of questions on my midterms and finals. If having these problems to look at helps you, then good. If not, feel free to ignore them. Midterm Exam #1 – Fall 1980 Problem 1 Rodney Random has just taken a job with Fasbux Financial consultants. His first task is to evaluate two bonds (A and B) with regard to “expected rate of return” and “risk of default.” He obtains 6 quarterly observations on the rates of return for each bond, measured as percents per year (see Table A). Let the sample mean R measure bond expected return, and sample variance s 2 measure bond risk. Most Fasbux clients want high rates of return and low risk. How will Rodney advise these clients with regard to Bonds A and B? (Show or summarize your calculations which you use to support your opinion.) 24 % 7 2 % 5 2 2 = = = = b b a a s R s R Problem 2 Pretend that the 12 observations in Table A are a single sample of n = 12 measurements of rate of return for one bond. A) Prepare a cell frequency table for the data R i , i = 1…12. Use Sturgis’ Rule and round down . Let your first interval be 0 – 3.99 with midpoint 2. Fill in Table B, then sketch the histogram of these data. B) Calculate the average rate of return for the 12 observations, using the appropriate formula for data grouped into cells (intervals). 33 . 6 = R Problem 3 Table A A B 4 6 3 5 5 7 1 10 8 2 14 7 Table B Interval M j f j f j /n 0 – 3.99 2 3 4 – 7.99 6 8 – 11.99 10 0.167 12 – 15.99 14 0 4 8 12 16 r f f/n Fig. A
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Ec 120A (Foster) OLD EXAMS p. 2 In the Venn diagram at right, S is the universe (sample space of an experiment), and event D C. A) Do events A, B, C, D and E partition of S? No B) What is Pr(B|A)? 0 C) What is Pr(C|D)? D) What is Pr(~B|E)? E) Shade the event ~D C. Problem 4 The EPA conducts an experiment in which 40 automobiles of varying horsepower are tested for exhaust emission standards violations. The cars are grouped into 3 horsepower categories: compact, midsize, and muscle cars. There are 20 compact, 15 midsize, and 5 muscle cars in the sample. The tests show that 1/4 of compacts, 1/3 of midsize, and 4/5 of muscle cars fail the tests. A) Fill in the empty cells in Table B with the correct number of cars. Cell e 6 has been filled in for illustration. B) The experiment consists of drawing a car from a set of 40 cars and observing its horsepower category and its test performance. There are obviously 6 possible outcomes e 1 … e 6 . What is Pr(e 1 )? 0.125 C) Event F is “Car fails test.” What is Pr(F)? 0.35 D) What is Pr(C2 F)? 0.125 What is Pr(C2 C3)? 0.50 E) The Bayesian question. One of the cars tested by the EPA is a still-secret Fosterfire Phaeton ZTX Sport Megahummer. You learn that the Fosterfire vehicle failed the test. What is the probability that the Fosterfire is a muscle car?
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