MidtermExam_EL6303Fall08

# MidtermExam_EL6303Fall08 - EL6303 Probability Theory:...

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EL6303 Probability Theory: Midterm Exam (Moon) October 30, 2008 Name Instructions: This exam consists of 40 short-answer and 2 full-length problems. For short-answer problems, you need show only your choice for answer by circling letter for it. You may use any blank space on page for any work needed to arrive at your choice. For full-length problems you must show all steps. Reference Information A + B = A B ± ; AB = A + B Binomial Random Variable: X B ( n;p ) = ) = np ; ± = p npq Poisson Approximation for X B ( n;p ) : P [ X = k ] e k k ! where ² = = np , n large, and p small. For Poisson random arrival process, ² = ct where c = average number of arrivals per unit time and t = time interval of interest. In such process, P [ ³ > t ] = e ct where ³ is the waiting time between arrivals. 1

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1. C A + C B + C ± =? (a) C (b) C (c) A (d) B 2. ² A + B ³ + ² A + B ³ =? (a) B (b) B (c) A (d) A 3. A + B C =? (a) A BC (b) AB C (c) A B C (d) ABC 4. A \ B = () A B C (a) True (b) False 5. S = f 1 ; 2 ; 3 ; 4 ; 5 ; 6 ; 7 ; 8 ; 9 ; 10 g : Which choice is a partition of S ? (a) A = f 1 ; 2 ; 3 ; 4 ; 5 g ; B = f 5 ; 6 ; 7 ; 8 ; 9 ; 10 g (b) A = f 1 ; 2 ; 3 ; 4 g ; B = f 7 ; 8 ; 9 ; 10 g (c) A = f 1 ; 2 ; 3 g ; B = f 8 ; 9 ; 10 g ; C = f 4 ; 5 ; 6 ; 7 g (d) None of the above 2
6. Given: A = f a 1 ;a 2 ;a 3 g ; B = f b 1 ;b 2 ;b 3 g . Cartesian Product: A B =? (a) f ( a 1 ;b 1 ) ; ( a 1 ;b 2 ) ; ( a 1 ;b 3 ) g (b) f ( a 1 ;b 1 ) ; ( a 1 ;b 2 ) ; ( a 1 ;b 3 ) ; ( a 3 ;b 1 ) ; ( a 3 ;b 2 ) ; ( a 3 ;b 3 ) g (c) f ( a 1 ;b 1 ) ; ( a 1 ;b 2 ) ; ( a 1 ;b 3 ) ; ( a 2 ;b 1 ) ; ( a 2 ;b 2 ) ; ( a 2 ;b 3 ) ; ( a 3 ;b 1 ) ; ( a 3 ;b 2 ) ; ( a 3 ;b 3 ) g (d) f ( a 3 ;b 1 ) ; ( a 2 ;b 2 ) ; ( a 1 ;b 3 ) g 7. Given a probability sample space S with events A;B;C where ( A [ B [ C

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## MidtermExam_EL6303Fall08 - EL6303 Probability Theory:...

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