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# t3818m1ans - University of Colorado Department of Economics...

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- 1 - University of Colorado Department of Economics Economics 3818 Midterm Examination Prof. Jeffrey S. Zax 27 September 2005 Solutions (14) 1. Consider two outcomes C and D, where Pr(C)=.3, Pr(D)=.5, Pr(C 1 D)=.3 (3) a. What is Pr(C c D)? Why? Pr(C c D) = Pr(C) + Pr(D) ! Pr(C 1 D) = .3 + .5 ! .3 = .5 (3) b. What is Pr(C * D)? Pr(C * D) = Pr(C 1 D) ' Pr(D) = .3 ' .5 = 3 ' 5 (2) c. What is Pr(D * C)? Pr(D * C) = Pr(C 1 D) ' Pr(C) = .3 ' .3 = 1 (2) d. Would you expect Pr(C * D) and Pr(D * C) to be the same? Why or why not? Ordinarily they would not be the same. They share the same numerator, Pr(C 1 D) , but their denominators would usually be different. They would be equal only if the numerator were zero or if Pr(C)=Pr(D). (2) e, Are C and D mutually exclusive? Why or why not? C and D are not mutually exclusive because the probability of their intersection is not zero. (2) f. Are C and D independent? Why or why not? C and D are not independent because .3 = P(C) P(C|D) = 3 ' 5.

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