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Unformatted text preview: e the number of shots the 4 player takes to score, including the scoring shot. (You can assume that each shot is independent of the others.) 326. In a game, the probability of a player scoring with a shot is (a) Find P(X = 3). (2) (b) Find the probability that the player will have at least three misses before scoring twice. (6) (c) Prove that the expected value of X is 4. (You may use the result (1 – x)–2 = 1 + 2x + 3x2 + 4x3......) (5) (Total 13 marks) 327. (a) Patients arrive at random at an emergency room in a hospital at the rate of 15 per hour throughout the day. Find the probability that 6 patients will arrive at the emergency room between 08:00 and 08:15. (3) (b) The emergency room switchboard has two operators. One operator answers calls for doctors and the other deals with enquiries about patients. The first operator fails to answer 1% of her calls and the second operator fails to answer 3% of his calls. On a typical day, the first and second telephone operators receive 20 and 40 calls respectively during an afternoon session. Using the Poisson distribution find the probability that, between them, the two operators fail to answer two or more calls during an afternoon session. (5) (Total 8 marks) 226 328. Dr. David Logan is conducting research to determine the effect on sleeping patterns of drinking coffee after dinner. A survey of a random sample of 60 persons chosen independently of each other was conducted to find if they sleep less soundly if they drink coffee after dinner. The results are shown below: Number of cups of coffee sleep is worse after dinner sleep is the same sleep is better 1 5 7 3 2 10 4 1 3 25 5 0 Dr. Logan wants to test the above data to determine whether sleeping patterns are independent of the number of cups of coffee after dinner. (a) Explain how he should test the data, mentioning the kind of test and the test statistic that should be used. (1) (b) Determine if the above data indicates that having coffee after dinner and sleeping soundly are independent at a 5% level of significance. (9) (Total 10 marks) 329. Let A and B be two non-empty sets, and A – B be the set of all elements of A which are not in B. Draw Venn diagrams for A – B and B – A and determine if B ∩ (A – B) = B ∩ (B – A). (Total 3 marks) 227 330. Consider the set × + . Let R be the relation defined by the following: + for (a, b) and (c, d) in × , (a, b) R (c, d) if and only if ad = bc, where ab is the product of the two numbers a and b. (a) Prove that R is an equivalence relation on × + . (4) (b) Show how R partitions × + , and describe the equivalence classes. (2) (Total 6 marks) 331. ABCD is a unit square with centre O. The midpoints of the line segments [CD], [AB], [AD], [BC] are M, N, P, Q, respectively. Let L1 and L2 denote the lines (MN) and (PQ), respectively. Consider the following symmetries of the square: U is a clockwise rotation about O of 2π; H is the reflection of the vertices of the square in the line L2; V is th...
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This note was uploaded on 06/24/2013 for the course HISTORY exam taught by Professor Apple during the Fall '13 term at Berlin Brothersvalley Shs.

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