251y0322 - 251y0322 10/27/03 ECO251 QBA1 SECOND HOUR EXAM...

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251y0322 10/27/03 ECO251 QBA1 SECOND HOUR EXAM March 21, 2003 Name: ____KEY_____________ Social Security Number: _____________________ Part I: (48 points) Do all the following: All questions are 2 points each except as marked. Exam is normed on 50 points including take-home. Please re-read, ‘Things that You should never do on an Exam or Anywhere Else, ‘ and especially recall that a probability cannot be above 1! The following joint probability table shows the relation between two sets of events. Let event A be that the individual is below 22 ( A is over 21), and the event 0 B be that the individual had no traffic violations in the last 18 months, the event 1 B be that the individual has one traffic violation in the last 18 months and the event 2 B be that the individual has 2 traffic violations over the last 18 months. No individuals in this pool of drivers has more than 2 violations. 01 . 18 . 41 . 06 . 12 . 22 . 2 1 0 A A B B B Note, to do the problems below, at least total the rows and columns - 00 . 1 07 . 30 . 63 . 60 . 40 . 01 . 18 . 41 . 06 . 12 . 22 . 2 1 0 A A B B B 1. The probability that someone who is over 21 has no traffic violations is (To 2 decimal places): a) .63 b) .60. c) .41 d) *.68 You have been asked for ( 29 ( 29 ( 29 683 . 60 . 41 . 0 0 = = = A P A B P A B P e) None of the above. 2. The probability that someone picked at random is over 21 and has no traffic violations is (To 2 decimal places): a) .63 b) .60. c) *.41 Joint probabilities are what the table shows! d) .68 e) None of the above. 3. The probability that someone chosen at random is either under 22 or has 2 violations is: a) .40 b) .06 c) .46 d) .47 e) *.41 ( 29 ( 29 ( 29 ( 29 41 . 06 . 07 . 40 . 2 2 2 = - + = - + = B A P B P A P B A P f) None of the above 1
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251y0322 10/27/03 00 . 1 07 . 30 . 63 . 60 . 40 . 01 . 18 . 41 . 06 . 12 . 22 . 2 1 0 A A B B B 4. Which two events are independent? a) A and A Note that ‘mutually exclusive’ and ‘independent are almost opposites. b) A and 2 B c) * A and 1 B . The definition of independence is ( 29 ( 29 A P B A P = 1 . In this case ( 29 60 . = A P and ( 29 ( 29 ( 29 60 . 30 . 18 . 1 1 1 = = = B P B A P B A P . But a better way to do this is to note that ( 29 ( 29 ( 29 ( 29 18 . 30 . 60 . 1 1 = = = B P A P B A P . d) A and 0 B e) A and 2 B f) None of these. 5. Which two events are mutually exclusive? a) * A and A Complements are always mutually exclusive. None of the other pairs have a joint probability of zero. b) A and 2 B c) A and 1 B . d) A and 0 B e) A and 2 B f) None of these. In questions 6 and 7 you need to know what ( 29 0 B P , ( 29 1 B P and ( 29 2 B P are to do the problems. Show your work. Solution: We can use the following table. ( 29
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251y0322 - 251y0322 10/27/03 ECO251 QBA1 SECOND HOUR EXAM...

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