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Unformatted text preview: MATH 218 FINAL EXAM Fall 2004 December 15, 2004 Instructions. • Show All Work. No credit in general for answers only, if there is work to be shown. Simplify answers to a fraction or decimal, and write this final answer in the box given, if one is provided. Keep at least 3 digits of accuracy after the decimal point. Use the back of the answer sheet for more space. • If you can’t do part (a) of some problem, but you need the answer for (b), then you can get partial credit for showing you know what to do. You could write, “Let p be the answer to (a),” and solve (b) in terms of p . • A calculator is allowed but it must not have any additional capabilities: no cell phones, Palm Pilots, etc. that can function as calculators. Problem 1. A survey of those households which have two registered voters found the following joint distribution for the number X of votes cast for Bush, and the number Y cast for Kerry, in the household: Y X 1 2 .05 .05 .35 1 .05 .10 2 .40 (a) What is the probability, among these households, that both reg- istered voters actually voted? (b) Are X and Y independent? State how you know. (c) Make a table of the marginal distribution of X . (d) Find the expected value of X . Problem 2. At an art exhibition there are 12 paintings of which 10 are authentic originals. A visitor selects a painting at random and before she decides to buy, she asks the opinion of an expert about the authenticity of the painting. The expert marks the painting REAL (if he believe it is authentic) or FAKE (if he believes it is a copy.) He is right in 90% of cases on average, both with authentic paintings and non-authentic copies. (a) Make a probability tree for this situation. (b) Given that the expert marks a painting FAKE, what is the prob- ability that it is authentic, and what is the probability it is a copy?...
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This homework help was uploaded on 02/05/2008 for the course MATH 218 taught by Professor Haskell during the Fall '06 term at USC.
- Fall '06