midterm2sol

# 6 cs 70 fall 2013 midterm 2 1 name sid alternate

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Unformatted text preview: s different. i. What is Pr[C]? Solution: 1 . z can be any value other than zero. 6 CS 70, Fall 2013, Midterm #2 1 Name: SID: Alternate interpretation: 3x−1 . 6 49 . Let x take on any non-zero value (6 possibilities) and y equal ii. What is Pr[A ∩ B]? 1 Solution: 36 . Both x and y are equal to 3 with probability ( 1 )2 . 6 1 Alternate interpretation: 49 . Both x and y are equal to 3 with probability ( 1 )2 . 7 iii. What is Pr[A ∩ C]? 1 Solution: 36 .This means that x = 3 and y = 1, which occurs with probability ( 1 )2 . 6 1 Alternate interpretation: 49 .This means that x = 3 and y = 1, which occurs with probability ( 1 )2 . 7 iv. What is Pr[B ∩ C]? 1 Solution: 36 . This means that y = 3 and x = 1, which occurs with probability ( 1 )2 . 6 1 Alternate interpretation: 49 . This means that y = 3 and x = 1, which occurs with probability ( 1 )2 . 7 v. Are A,B,C pairwise independent? Yes No Are A,B,C pairwise independent? Alternate interpretation: Yes No (g) (5 points) Suppose A and B are disjoint events such that P[A] ￿= 0 and P[B] ￿= 0. i. What is Pr[A ∩ B]? Solution: 0. The events are disjoint so their intersection is empty (it contains no sample points). ii. Can A and B be independent? Yes No Solution...
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## This document was uploaded on 01/28/2014.

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