HW+2+Solutions

# HW+2+Solutions - ISyE 2027 Fall 2011 Homework 2 Solutions 1...

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Unformatted text preview: ISyE 2027 Fall 2011 Homework 2 Solutions 1. Let A and B be events. a. P ( A ) b. Ω c. A ∩ B = ϕ d. P ( A ∩ B ) = 0 e. ω ∈ Ω f. A ∪ B g. A c h. 1- P ( A ) 2. a. A and B are disjoint. b. Probability of event B. c. Set of all outcomes. d. ω is an outcome. e. A or B . Otherwise A union B . f. A and B . Otherwise A intersect B . g. Probability that A does not occur. 3. a. F = {{ a } , { b, c } , { a, b, c } , ϕ } b. F = {{ a } , { b } , { c } , { a, c } , { a, b } , { b, c } , { a, b, c } , ϕ } 4. P (Ω) = 1 , ⇒ 1 10 + 3 10 + c = 1 ⇒ c = 3 5 5. P (Ω) = 1 , ⇒ c + c · 2 2 + c · 3 2 = 1 ⇒ c = 1 14 6. There are no values of c such that the axioms are satisfied. Note that P ( ω 1 ) =- c , P ( ω 2 ) = 0 , P ( ω 3 ) = c . For all non-zero values of c , either ω 1 or ω 3 has a negative probability which contradicts axiom 1. Furthermore, if c = 0 , the P (Ω) = 0 which contradicts axiom 3....
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HW+2+Solutions - ISyE 2027 Fall 2011 Homework 2 Solutions 1...

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