mid1(07) - nctuee07f Stochastic Processes Midterm 1 1:00 pm...

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Stochastic Processes Midterm 1 1:00 pm – 3:20 pm, 10/23/07 IMPORTANT: Remember to write down your id number and your name. There are 4 problem sets with 110 points in total. Please provide detailed explanations/reasonings with your answers. Correct answers with- out any explanations will carry NO credits. On the other hand, wrong answers with correct reasonings will get partial credits. You may need the following formulas: Let x = [ X 1 ,X 2 , ··· ,X n ] be a real Gaussian random vector with mean vector m x and covariance matrix K x . Then, the joint pdf f x ( x ) is given by f x ( x ) = 1 (2 π ) n/ 2 det( K x ) 1 / 2 exp ± - 1 2 ( x - m x ) T K - 1 x ( x - m x ) . The joint moment generating function for N random variables X 1 ··· X N is defined by θ ( t 1 ,t 2 , ··· ,t N ) = E " exp ˆ N X i =1 t i X i !# . The correlation coefficient ρ between random variables X and Y is defined by ρ , E £ ( X - μ X )( Y - μ Y ) / σ X σ Y , where μ X
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mid1(07) - nctuee07f Stochastic Processes Midterm 1 1:00 pm...

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