final_2015 - MS&E 221 Ramesh Johari Final Examination...

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MS&E 221 Final Examination Ramesh Johari March 16, 2015 Instructions 1. Take alternate seating. 2. Answer all questions in the blue books provided. If needed, additional blue books will be available at the front of the room. Answers given on any other paper will not be counted. 3. The examination begins at 12:15 pm, and ends at 3:15 pm. 4. You may only use the following additional aids on the exam: (a) textbook(s); (b) lecture notes and/or other handouts; and (c) your own notes. 5. You may not : use software aids (e.g., Matlab, R, etc.); access the Internet; or consult with others. 6. If your notes and handouts are only on a laptop, tablet, or other device, you may use that device, but without networking/wifi enabled. 7. The exam will be scored out of 70 points (you receive two points for showing up). 8. You will receive partial credit, so please show your work—but also note that any incorrect answer will be marked down accordingly. 9. Pace yourself! Honor Code In taking this examination, I acknowledge and accept the Stanford University Honor Code. NAME (signed) NAME (printed) 1
Useful Formulas 1. If X is a geometric random variable with parameter p , then the pmf of X is: P ( X = k ) = (1 - p ) k - 1 p, k 1 . 2. If X is a binomial random variable with parameters p and n , then the pmf of X is: P ( X = k ) = n k p k (1 - p ) n - k = n ! k !( n - k )! p k (1 - p ) n - k , 0 k n. 3. If T is an exponentially distributed random variable with mean 1 , then the density of T is given by f T , where: f T ( t ) = λe - λt , t 0 . 4. If S is a random variable with a gamma distribution of parameters n and λ , where n is a positive integer, then the density of S is given by f S , where: f S ( s ) = λe - λs ( λs ) n - 1 ( n - 1)! , s 0 . 5. If N is a Poisson random variable of parameter λ , then the pmf of N is: P ( N = k ) = e - λ λ k k ! , k 0 .

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