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Stat104_studyguide_part2_SOLUTIONSv3

Stat104_studyguide_part2_SOLUTIONSv3 - Stat 104...

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Study Guide Solutions, part 2 Stat 104: Quantitative Methods for Economists
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1) The table below shows, for credit card holders with one to three cards, the joint probabilities for number of cards owned (X) and number of credit purchases made in a week (Y). I have already calculated part of the marginal distribution for X. Y 0 1 2 3 4 1 0.08 0.13 0.09 0.06 (3) 0.4 X 2 0.03 0.08 0.08 (2) 0.07 0.35 3 0.01 (1) 0.06 0.08 0.08 a) For this to be a legal probability table, the sum of all the joint probabilities has to be what value? 1 b) Fill in the empty cells in the above joint probability table. (1) = 0.02 (2) = 0.09 (3) = 0.04 c) What is the probability that X equals Y ? P(X=1 and Y=1)+P(X=2 and Y=2) +P(X=3 and Y=3)=.13+.08+.08 = 0.29 d) Are X and Y are independent? Why? P(X=1|Y=1) = 0.13/0.23 = 0.5652 which does not equal P(X=1)=0.40 So Not Independent. 2) Suppose the sample mean score on a national test is 500 with a standard deviation of 100. If each score is increased by 25%, what are the new mean and standard deviation? (a) 500, 100 (b) 525, 100 (c) 525, 125 (d) 625, 100 (e) 625, 125
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3) A random variable Y has the following probability distribution: y -1 0 1 2 p(y) 3k 7k 0.4 0.1 The value of the constant k is: 4) If X and Y are independent random variables, then The following is used for the next 3 questions. Let X be a discrete random variable with the following probability function x -1 1 2 P(X=x) .2 .3 .5 5) What is P(0 < X < 3)? 6) The mean μ (expected value) of X is a) 4 b) 1.5 c) -1 d) 2.7 e ) 1.1
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7) The variance of X is Questions 8-10 were just repeats of the above three questions. 11) Which of the following is a legal probability table ? 12) A television game show has three payoffs with the following probabilities: Payoff ($) : 0 1000 10,000 Probability : .6 .3 .1 What are the expected value and standard deviation for the payoff variable ?
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13) Alex, Alicia, and Juan fill orders in a fast-food restaurant. Alex incorrectly fills 20% of the orders he takes. Alicia incorrectly fills 12% of the orders she takes. Juan incorrectly fills 5% of the orders he takes. Alex fills 30% of all orders, Alicia fills 45% of all orders, and Juan fills 25% of all orders. An order has just been filled. We know P(Wrong|Alex) = .2, P(Wrong|Alicia)=.12 and P(Wrong|Juan)=.05. We also know that P(Alex)=.3, P(Alicia)=.45 and P(Juan)=.25. Using P(A|B) = P(A and B)/P(B) we can build the following table: a. What is the probability that Alicia filled the order? 0.45 b. If the order was filled by Juan, what is the probability that it was filled correctly? P(correct|Juan) = P(correct and Juan)/P(Juan) = .2375/.25 = 0.95 (or P(wrong | Juan) = 1-P(correct|Juan) = 1 - .05) c. Who filled the order is unknown, but the order was filled incorrectly. What are the revised probabilities that Alex, Alicia, or Juan filled the order?
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