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# 07f - STATISTICS 401 Section 2 Final Exam ID Fall 2007 NAME...

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STATISTICS 401 Section 2 Final Exam Fall 2007 ID: NAME: . Directions: This examination consists of 7 problems. Write all of your answers in the space provided. If you need more space, use the back of the pages. You may use any notes or books you wish. You have 1 hour and 50 minutes. Partial credit will be assigned where appropriate, but you must show all your work. This is a 100-point test. The point value of each problem is indicated. GOOD LUCK! Problem: 1 2 3 4 5 6 7 Total Possible Points: 16 15 10 18 12 16 13 100 Score: 1

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Problem 1. [16 points, 2 for each of the 8 questions.] 1. Suppose the events A 1 , A 2 , A 3 , A 4 , A 5 , A 6 , and A 7 partition the sample space of an experiment (i.e. they are mutually exclusive and exhaustive) and that they are equally likely. (a) Find P ( A 1 A 4 ) (b) Find P ( A 3 A 5 A 6 ). 2. Suppose P ( A ) = 0 . 25 , P ( B ) = 0 . 62 , P ( C ) = 0 . 11, and we are given that P ( A B ) = 0 . 17, P ( A C ) = 0 . 02, and P ( B C ) = 0 . 63. (a) Find P ( A C ) (b) Find P ( B C ) 3. Suppose 10% of all a certain type of software widgets have connectivity problems. Suppose that a simple random sample of 10 such widgets are installed. (a) Let Y denote the number of them that have connectivity problems. The distribution of Y is (choose one) (i) binomial (ii) hypergeometric (iii) negative binomial (iv) Poisson (b) Find the probability that Y = 0. (c) Suppose that the 10 widgets are tested and it is found that 2 of them have connectivity problems. A customer purchases 3 widgets. Let X denote the number of them that have connectivity problems. The distribution of X is (choose one) (i) binomial (ii) hypergeometric (iii) negative binomial (iv) Poisson (d) Find the probability that X = 2. Problem 2. [15 points, 3 for each of the 5 parts.] In a popular local restaurant 65% of the customers order \$7.50 meals, while 35% order \$10.00 meals. Let X, Y denote the type of meal and the amount of tip left, respectively, by the next customer to walk in. The conditional probabilities for the amount of tip left, given the type of meal chosen, are y \$1.00 \$1.50 \$2.00 p Y | X =7 . 50 ( y ) 0.7 0.3 0 p Y | X =10 . 00 ( y ) 0.05 0.65 .3 1. Find the joint probability mass function of X, Y . 2
2. Find the regression function of Y on X .

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07f - STATISTICS 401 Section 2 Final Exam ID Fall 2007 NAME...

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