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ecen303_hw9 - Z and T 3(20 Points Let X and Y be two...

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ECEN 303: Random Signals and Systems Spring 2010 Homework #9 Assigned date: Thursday April 29 in class Due date: You are not required to turn in your homework. Solutions will be posted on the course website on Monday May 3. Reading assignment: Chapters 6.1–6.3 of Ross Required exercises: 1. (20 Points) The joint PDF of X and Y is f ( x, y ) = 1 , 0 < x < 1 , 0 < y < 1 0 , otherwise (a) Find the PDFs of X and Y . Are X and Y independent? (b) Let Z = X + Y . Find the PDF and the expectation of Z . 2. (20 Points) Let X and Y be two independent, continuous random variables with PDF f X and f Y , respectively. Let Z = max { X, Y } and T = min { X, Y } . Find the PDFs of
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Unformatted text preview: Z and T . 3. (20 Points) Let X and Y be two jointly continuous random variables. Show that E [ X + Y ] = E [ X ] + E [ Y ] no matter X and Y are independent or not. 4. (20 Points) Let X and Y be two independent Gaussian random variables with parameters ( μ X ,σ 2 X ) and ( μ Y ,σ 2 Y ), respectively. Find the PDF of Z = X + Y . 5. (20 Points) Let X and Y be two independent random variables, both uniformly distributed over (0 , 1). Use the convolution formula to calculate the PDF of Z = X + Y . 1...
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