HW+2+Solutions

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

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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. c. A B = d. P ( A B ) = 0 e. 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. 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 } , } b. F = {{ a } , { b } , { c } , { a, c } , { a, b } , { b, c } , { a, b, c } , } 4. P () = 1 , 1 10 + 3 10 + c = 1 c = 3 5 5. P () = 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 ( 1 ) =- c , P ( 2 ) = 0 , P ( 3 ) = c . For all non-zero values of c , either 1 or 3 has a negative probability which contradicts axiom 1. Furthermore, if c = 0 , the P () = 0 which contradicts axiom 3....
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HW+2+Solutions - ISyE 2027 Fall 2011 Homework 2 Solutions...

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