131A_1_131A_1_practice-problem-soln-part1-2010

# 131A_1_131A_1_practice-problem-soln-part1-2010 - EE 131A...

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EE 131A Midterm Solutions Probabilities Fall 2004 Instructor: Vwani Roychowdhury 1. Problem 1. For the sum to be 8, we could have (2 , 6), (3 , 5), (4 , 4), (5 , 3), (6 , 2). (a) P [ sum =8 | 2 nd Die ]=2 × 1 / 8 × 1 / 4+3 × 1 / 8 × 1 / 8=7 / 64. (b) Similarly, P [ sum =8 | 1 st Die ]=5 / 36; P [ sum =8 | 3 rd Die ]=2 × 1 / 3 × 1 / 12 + 3 × 1 / 12 × 1 / 12 = 11 / 144. So P [ sum =8 ]= P [ sum =8 | 1 st Die ] · P [1 st Die ]+ P [ sum =8 | 2 nd Die ] · P [2 nd Die ] + P [ sum =8 | 3 rd Die ] · P [3 rd Die ]=1 / 3 × (5 / 36 + 7 / 64 + 11 / 144) = 187 / 1728 . (c) P [1 st Die | (6 , 6)] = P [(6 , 6) | 1 st Die ] · P [1 st Die ] 3 i =1 P [(6 , 6) | ith Die ] P [ ith Die ] = 1 / 3 × 1 / 6 × 1 / 6 1 / 3(1 / 36+1 / 16+1 / 9) =4 / 29. 2. Problem 2. Let B denote the brown gene and b denote the blue gene. Since Smith’s sister has blue eyes ( bb ) and the parents have brown eyes, both his

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## This note was uploaded on 01/08/2011 for the course EE 131 taught by Professor R during the Spring '10 term at UCLA.

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131A_1_131A_1_practice-problem-soln-part1-2010 - EE 131A...

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