221_10_final

221_10_final - MS&E 221 Ramesh Johari Final Examination...

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Final Examination Ramesh Johari March 15, 2010 Instructions 1. Take alternate seating. 2. Answer all questions in the blue examination books. Answers given on any other paper will not be counted. 3. The examination begins at 8:30 am, and ends at 11:30 am. 4. No laptop computers or networked devices are allowed, but you may use any other non- human aids you wish. 5. Show your work! Partial credit will be given for correct reasoning. Honor Code In taking this examination, I acknowledge and accept the Stanford University Honor Code. NAME (signed) NAME (printed) 1
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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 ) = p n k P 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
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221_10_final - MS&E 221 Ramesh Johari Final Examination...

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