final2009

final2009 - NAME: NetID: Signature: 332:226 Probability and...

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Unformatted text preview: NAME: NetID: Signature: 332:226 Probability and Stochastic Processes Final Examination May 8, 2009 MAKE SURE TO READ BOTH SIDES OF THIS EXAM PAPER. You have 180 minutes to answer the following questions in the notebooks provided. You are permitted to use one double sided handwritten sheet of notes but no other resources. Make sure that you have included your name, RU NetID and signature at the top of this exam paper (5 points) and on the cover of each blue book used (5 points). Read each question carefully. All statements must be justified. Computations should be simplified as much as possible. Gaussian probabilities should be expressed in terms of the 8( · ) or Q ( · ) functions. When you finish, please submit your blue book(s), with this exam paper inside. 1. 40 points ANSWERS IN THE BOX: Each of these questions must be answered by filling in the corresponding boxes below. No justification is needed. No credit will be given for answers written in the blue book. (a) You flip a fair coin 4 times. Each flip is heads h or tails t . What is the probability of the sequence htth ? (b) X is a continuous uniform ( , 5 ) random variable. What is P [ X < 2]? (c) K is a Poisson random variable with E [ K ] = 10. What is P [ K = E [ K ]] (d) Y is a Gaussian ( 10 , 1 ) random variable. What is P [ Y = E [ Y ]] (a) (b) (c) (d) 2. 40 points In the Monty Hall game, a new car is (equiprobably) hidden behind one of three closed doors while a goat is hidden behind each of the other two doors. The game proceeds as follows: • You randomly select a door. • The host, Monty Hall (who knows where the car is hidden), opens one of the two doors you didn’t select to reveal a goat. • Monty then asks you if you would like to switch your selection to the other unopened door....
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This note was uploaded on 02/13/2011 for the course 332 226 taught by Professor Staff during the Spring '08 term at Rutgers.

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final2009 - NAME: NetID: Signature: 332:226 Probability and...

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