131A_1_131A_1_practice-problem-soln-part1-2010

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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

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

Page1 / 3

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online