quiz_sol - Probability and Stochastic Processes A Friendly...

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Probability and Stochastic Processes A Friendly Introduction for Electrical and Computer Engineers Second Edition Quiz Solutions Roy D. Yates and David J. Goodman May 22, 2004 The M ATLAB section quizzes at the end of each chapter use programs available for download as the archive matcode.zip . This archive has programs of general pur- pose programs for solving probability problems as well as specific .m files associated with examples or quizzes in the text. Also available is a manual probmatlab.pdf describing the general purpose .m files in matcode.zip . We have made a substantial effort to check the solution to every quiz. Nevertheless, there is a nonzero probability (in fact, a probability close to unity) that errors will be found. If you find errors or have suggestions or comments, please send email to [email protected] . When errors are found, corrected solutions will be posted at the website. 1
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Quiz Solutions – Chapter 1 Quiz 1.1 In the Venn diagrams for parts (a)-(g) below, the shaded area represents the indicated set. M O M O T M O T T c (2) M M O M O T M O T M O T (4) R M (4) R M (6) T c M Quiz 1.2 (1) A 1 ={ vvv, vv d ,v d v, v dd } (2) B 1 d vv, d v d , v, ddd } (3) A 2 d , d d v d } (4) B 2 v d , } (5) A 3 vvv, } (6) B 3 v d d v d } (7) A 4 d d d vv, v , d v d , v } (8) B 4 , d v d } Recall that A i and B i are collectively exhaustive if A i B i = S . Also, A i and B i are mutually exclusive if A i B i = φ . Since we have written down each pair A i and B i above, we can simply check for these properties. The pair A 1 and B 1 are mutually exclusive and collectively exhaustive. The pair A 2 and B 2 are mutually exclusive and collectively exhaustive. The pair A 3 and B 3 are mutually exclusive but not collectively exhaustive. The pair A 4 and B 4 are not mutually exclusive since d v d belongs to A 4 and B 4 . However, A 4 and B 4 are collectively exhaustive. 2
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Quiz 1.3 There are exactly 50 equally likely outcomes: s 51 through s 100 . Each of these outcomes has probability 0 . 02. (1) P [{ s 79 }] = 0 . 02 (2) P [{ s 100 }] = 0 . 02 (3) P [ A ]= P [{ s 90 ,..., s 100 }] = 11 × 0 . 02 = 0 . 22 (4) P [ F P [{ s 51 s 59 }] = 9 × 0 . 02 = 0 . 18 (5) P [ T 80 P [{ s 80 s 100 }] = 21 × 0 . 02 = 0 . 42 (6) P [ T < 90 P [{ s 51 , s 52 s 89 }] = 39 × 0 . 02 = 0 . 78 (7) P [ a C grade or better P [{ s 70 s 100 }] = 31 × 0 . 02 = 0 . 62 (8) P [ student passes P [{ s 60 s 100 }] = 41 × 0 . 02 = 0 . 82 Quiz 1.4 We can describe this experiment by the event space consisting of the four possible events VB , VL , DB , and DL . We represent these events in the table: VD L 0 . 35 ? B ?? In a roundabout way, the problem statement tells us how to fill in the table. In particular, P [ V ] = 0 . 7 = P [ ] + P [ ] (1) P [ L ] = 0 . 6 = P [ ] + P [ ] (2) Since P [ 0 . 35, we can conclude that P [ 0 . 35 and that P [ 0 . 6 0 . 35 = 0 . 25. This allows us to fill in two more table entries: L 0 . 35 0 . 25 B 0 . 35 ? The remaining table entry is filled in by observing that the probabilities must sum to 1. This implies P [ 0 . 05 and the complete table is L 0 . 35 0 . 25 B 0 . 35 0 . 05 Finding the various probabilities is now straightforward: 3
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(1) P [ DL ]= 0 . 25 (2) P [ D L P [ VL ]+ P [ P [ DB 0 . 35 + 0 . 25 + 0 . 05 = 0 . 65.
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This homework help was uploaded on 04/09/2008 for the course ENGR, STAT 320, 262, taught by Professor Harris during the Spring '08 term at Purdue.

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quiz_sol - Probability and Stochastic Processes A Friendly...

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