S09 - IE 336 Feb. 25, 2009 Name: Test #1 1. Let f (x, y ) =...

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IE 336 Feb. 25, 2009 Name: Test #1 1. Let f ( x,y ) = ( c ( x + y ) 2 - 2 x 2 , 0 y 2 0 otherwise be the joint pdf of two continuous random variables X and Y . (a) Determine the value of the constant c . (b) Are the random variables X and Y independent? Explain. (c) Compute E ( Y ) and E ( XY ). 1
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IE 336 Feb. 25, 2009 Name: 2. Let X be a stationary Markov chain with states { 4 , 7 , 8 } . Let P = q 2 r 0 . 5 0 . 3 p 0 . 4 p 0 . 5 q be the one-step transition matrix of the Markov chain X (rows and columns of matrix P are ordered in the same way the states are, i.e. the first row/column corresponds to state 4, the second row/column corresponds to state 7, and the third row/column corresponds to state 8). Clearly p 74 = P ( X 1 = 4 | X 0 = 7) = 0 . 3, p 87 = P ( X 1 = 7 | X 0 = 8) = 0 . 5, etc. (a) Compute p , q , and r and determine the transition diagram of this Markov chain.
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This note was uploaded on 05/05/2011 for the course IE 336 taught by Professor Bruce,s during the Spring '08 term at Purdue University-West Lafayette.

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S09 - IE 336 Feb. 25, 2009 Name: Test #1 1. Let f (x, y ) =...

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