mid2 - 332:321 Probability and Stochastic Processes...

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332:321 Probability and Stochastic Processes Examination 2 November 22, 2004 You have 80 minutes to answer the following questions in the notebooks provided. You are permitted 1 double-sided sheet of notes. Make sure that you have included your name, Rutgers netid and signature in each book used. (5 points) Read each question carefully. All statements must be justified. Computations should be simplified as much as possible. The following table may be helpful: x 0 . 0 0 . 25 0 . 5 0 . 75 1 . 0 1 . 25 1 . 50 1 . 75 2 . 0 2 . 25 2 . 50 8( x ) 0 . 50 0 . 599 0 . 692 0 . 773 0 . 841 0 . 894 0 . 933 0 . 960 0 . 977 0 . 988 0 . 994 1. 40 points SHORT ANSWER: Each part is a separate problem. (a) Y is a Gaussian = 5 , σ = 10 ) random variable. Calculate P [ Y > 20]. (b) X is a Gaussian = 0 , σ = 1 ) random variable. Z is a Gaussian ( 0 , 4 ) random variable. X and Z are independent. Let Y = X + Z . Find the correlation coefficient ρ of X and Y . Are X and Y independent? (c)
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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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