2027Hmwk2

# 2027Hmwk2 - ISyE 2027 Probability with Applications Fall...

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Unformatted text preview: ISyE 2027 Probability with Applications Fall 2011 R. D. Foley Homework 2 August 28, 2011 due on Monday 1. Give mathematical expressions each of the following: (a) the probability of A , (b) the set of all possible outcomes, (c) the events A and B are dis- joint, (d) the events A and B are mutually exclusive, (e) ω is an outcome, (f) either the event A or the event B . (g) the complement of the event A , (h) the probability that A does not occur. 2. Express the following in words: (a) AB = ∅ , (b) P ( B ) , (c) Ω , (d) ω ∈ Ω . (e) A ∪ B , (f) A ∩ B . (g) P ( A c ) . 3. Let Ω = { a , b , c } . (a) Suppose { a } ∈ F . What other subsets of Ω must be in F so that the event axioms described in our text hold? In other words, give me the smallest F that contains { a } and satisfies the axioms. (b) Suppose both { a } and { c } are in F . What other subsets of Ω need to be in F so that the event axioms hold? 4. Suppose Ω = { ω 1 , ω 2 , ω 3 } , P { ω 1 } = 1 / 10, P { ω 2 } = 3 / 10 , and P { ω 3 } = c ....
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2027Hmwk2 - ISyE 2027 Probability with Applications Fall...

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