MidtermExam_EL6303Fall08

MidtermExam_EL6303Fall08 - EL6303 Probability Theory:...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 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
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 11

MidtermExam_EL6303Fall08 - EL6303 Probability Theory:...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online