Mathematics > EXAM > Sample-final - Ohio State University STAT 4201 (All)

Sample-final - Ohio State University STAT 4201

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Final Exam This is an old final exam from a similar course I taught at Duke. Note that it was a 3 hour exam, so quite a bit longer than ours, and that problem 7 is from section 6.5, which we did no... t cover. • Do not open this test booklet until you are directed to do so. • You will have 3 hours to complete the exam. • This is a closed book exam. No calculators, notes, or any other form of assistance is allowed. Read each question carefully and answer it in the space provided. YOU MUST SHOW ALL OF YOUR WORK TO RECEIVE FULL CREDIT! Please be clear and concise in your solutions. • In problems involving the standard normal cumulative distribution function Φ, you may leave your answer in the form Φ √a−bc def ; that is, you don’t have to simplify the fraction or evaluate what is under a square root sign. Problem Points Score 1 20 2 18 3 15 4 15 5 10 6 12 7 10 Total 100 Name: 1 Math 135 May 1, 2012 Final Exam Question 1 (20 pts). Suppose (X, Y ) have joint density f(x, y) =    ce−2y if 0 < x < y 0 otherwise. a) Find c. b) Find E[XeY ]. c) Compute the marginal density fX(x). d) Compute P(X + Y < 2) 2 Math 135 May 1, 2012 Final Exam Question 2 (18 pts). A niche video store sells two types of movies: zombie movies and vampire movies. People tend to strongly prefer one genre over the other, so we can classify the customers into zombie-lovers and vampire-lovers. Assume that these two types of customers arrive at the store according to two independent Poisson processes. Since vampires are more popular lately, vampire customers arrive at a rate of 3 per hour, while zombie customers arrive at a rate of only 2 per hour. a) Find the probability that exact [Show More]

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