131A_1_ds1_2010fall

# 131A_1_ds1_2010fall - A ∪ B c ∪ C c c in each of the...

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EE 131A Discussion Set 1 Probability Wednesday, September 29, 2010 Instructor: Lara Dolecek and Friday, October 1, 2010 Reading: Chapter 2 of Probability, Statistics, and Random Processes by A. Leon-Garcia 1. Venn diagram. Problem 2.13, page 82 of ALG 2. Balls and buckets. Problem 2.50, page 86 of ALG 3. Bonferroni’s inequality. Suppose A and B are two events. Use the axioms of probability to prove the following: P ( A B ) P ( A ) + P ( B ) - 1 Show that the probability that one and only one of the events A or B occurs is P ( A ) + P ( B ) - 2 P ( A B ) 4. Set operations. Find P (
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Unformatted text preview: A ∪ ( B c ∪ C c ) c ) in each of the following cases: • A , B , C are mutually exclusive events and P ( A ) = 4 / 7. • P ( A ) = 1 / 2, P ( B ∩ C ) = 1 / 3, P ( A ∩ C ) = 0. • P ( A c ∩ ( B c ∪ C c )) = 0 . 65. 5. Coin tossing. For four tosses of a fair coin, deﬁne the sample space. Find the proba-bilities of the following events: • the sequence HHHH? • the sequence HTHT? • seeing two heads and two tails ? • seeing three heads and one tail? 1...
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## This note was uploaded on 01/16/2011 for the course EL ENGR 131A taught by Professor Dolecek during the Fall '10 term at UCLA.

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