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Unformatted text preview: Kata Bognar email@example.com Economics 41 Statistics for Economists UCLA Fall 2010 Final Exam- suggested solutions - Part I - Multiple Choice Questions (4 points each) 1. Two unbiased four-sided dice are rolled. What is the probability that the sum of the two numbers on the dice is 3? D (a) 1/16 (b) 3/16 (c) 4/16 (d) none of the above Explanation: The sum of the numbers on the two dice is 3 if the first die shows 1 and the second shows 2 or if the first die shows 2 and the second shows 1. These outcomes happen with probability 1/16, each, so the probability of the event above is 2/16. 2. Suppose that A and B are events and P ( B ) = 0 . 6, P ( A | B ) = 0 . 5, then P ( B | A ) = D (a) 0.3 (b) 0.5 (c) 0.6 (d) there is not enough information to solve the above Explanation: One can calculate P ( A B ) given the information above, however determining the value of P ( A ) is not possible. Hence, there is not enough information to find P ( B | A ) . 3. At a grocery store, eggs come in cartons that hold a dozen eggs. Experience indicates that 76% of the carton have no broken eggs, 20% have one broken egg, 3% have two broken eggs and 1% have three or more broken eggs. An egg selected random from a cartoon and is found to be broken. What is the probability that this is the only broken egg in the carton? C (a) 1/5 (b) 1/6 (c) 5/6 (d) none of the above Explanation: Denote by B the event that the is a broken egg in the carton and A the event that there is only one broken egg in the carton. Then we have to determine P ( A | B ) . By the conditional probability formula P ( A | B ) = P ( A B ) /P ( B ) = 0 . 2 / (0 . 2 + 0 . 03 + 0 . 01) = 5 / 6 . 4. Two events are said to be independent if the occurrence of one event: B (a) affects the probability of the occurrence of the other event (b) does not affect the probability of the occurrence of the other event (c) means that second event cannot occur (d) means that second event is definite to occur 5. Let X denote the number of corporations in a random sample of 4 that provide retirement benefits. Assume that the population consists of 16 corporations, of which 3 provide retirement benefits. Then X is a hypergeometric random variable with N = 16 ,r = 3 , and n = 4 . The probability that at most one of the selected firms offers retirement benefits is: A 1 (a) 0.8643 (b) 0.7711 (c) 0.1357 (d) 4091 Explanation: By the hypergeometric probability formula, P ( X = x ) = ( 13 4- x )( 3 x ) ( 16 4 ) . Then the probability P ( X 1) = P ( X = 0) + P ( X = 1) = ( 13 4 )( 3 ) ( 16 4 ) + ( 13 3 )( 3 1 ) ( 16 4 ) = 0 . 8643 . 6. In a survey of 300 college graduates x % reported that they entered a profession closely related to their college major. A random sample of n out of these 300 students selected with replacement....
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This note was uploaded on 12/28/2010 for the course ECON 41 taught by Professor Guggenberger during the Fall '07 term at UCLA.
- Fall '07