midterm1+fall+2010+solutions

midterm1+fall+2010+solutions - ECI 114 Fall 2010 Name _...

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ECI 114 Fall 2010 Name _____________________________ Midterm 1 Solutions (100 points): October 20, 2010 SHOW your work. It is not necessary to give a final numerical answer like “12” unless specifically asked; you just need to have the correct expression like “4!/2!”. Please circle or otherwise highlight your answer. Turn in your “crib sheet” with your exam. GOOD LUCK! _____________________________________________________________________________ _ 1. For each of the following statements, circle the letter “T” if it is true and “F” if it is false. (14 points) T F a. For a certain sample of 25 observations and a mean of 10, it is known that Σ y i 2 = 2625. The variance of this sample is 5. 2 . 5 24 125 24 10 * 25 2625 1 2 2 2 2 = = - = - - = N Y N y s i T F b. If A and B are collectively exhaustive, then Pr(A B) = Pr(A) + Pr(B). Would be true if A and B are mutually exclusive , since Pr(A∩B) = . T F c. If events A, B, and C are independent, then Pr(A) = Pr(A B C)/Pr(B C). If events A, B, and C are independent,[Pr(A B C]=Pr(A)Pr(B)Pr(C)=Pr(A)Pr(B C) T F d. If S = {the outcome of the roll of a balanced die} = {1, 2, 3, 4, 5, 6}, then the set containing the two events {(E P’), (P O)}, where P = prime, E = even, O = odd, is a partition of S (count 1 as a prime). P={1,2,3,5}; E={2,4,6}; O={1,3,5}. E P’={2,4,6}, P O={1,3,5}. Because these two sets are ME and CE, they constitute a partition. T F e. For any event A, (A S) (A’ S) = S, where S represents the entire sample space. A S = A, A’ S = A’, and A A’ = S by definition of complement. T F f. Since the expectation operator is linear, E[5X 2 ] = 5E[X*X] = 5(E[X]) 2 . X
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midterm1+fall+2010+solutions - ECI 114 Fall 2010 Name _...

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