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131A_1_MidtermInClass

131A_1_MidtermInClass - EE 131A Probability Instructor Lara...

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EE 131A Fall 2010 Midterm Probability Wednesday, October 27, 2010 Instructor: Lara Dolecek Maximum score is 100 points. You have 110 minutes to complete the exam. Please show your work. Good luck! Your Name: Your ID Number: Name of person on your left: Name of person on your right: Problem Score Possible 1 6 2 15 3 8 4 12 5 15 6 8 7 8 8 10 9 18 Total 100 1
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1. (6 pts) Suppose P ( A ) = 1 / 3, P ( A B ) = 1 / 2 and P ( A B ) = 1 / 5. Find P ( B ). 2
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2. (4+5+6 pts) Let X and Y be independent and uniform on { 1 , 2 , . . . M } . Find (a) P ( X = Y ). (b) P ( X Y ). (c) pmf of U where U = | X - Y | . 3
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3. (4+4 pts) Suppose X and Y are independent random variables with finite first and second moments. Let Z = 3 X + 5 Y . Compute mean and variance of Z in terms of E ( X ) , E ( Y ) , V AR ( X ) and V AR ( Y ). 4
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4. (12 pts) A 52-card deck consists of 4 suits (clubs, diamonds, hearts, spades), and each suit has 13 cards (2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A). Suppose you are dealt a poker hand consisting of 5 cards. Compute the probability of getting flush. Flush hand is 5 cards of the same suit.
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