part3 - ECE 863 Analysis of Stochastic Systems Fall 2001...

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

View Full Document Right Arrow Icon
1 ECE 863 – Analysis of Stochastic Systems Fall 2001 Solutions for Homework Set #1 Michigan State University Department of Electrical & Computer Engineering Problem 1 2.4 (a) The sample space S = set of ordered pairs which can be expressed as: (i, 1) (i, 2) …… (i, i), for i = 1, 2, 3, 4, 5, 6 Therefore: S1 , 1 2,1 2,2 3,1 3,2 3,3 6,1 6,2 6,3 6,4 6,5 6,6 = bg m b g b g b g b g b g b g b g b g b gr , ,, ,,, ,, ± 2.4 (b) 4,1 , 4,2 , 4,3 , 4,4 b g b g b g mr 2.4 (c) 3,3, 4,3, 5,3, 6,3 2.4 (d)
Background image of page 1

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

View Full DocumentRight Arrow Icon
2 Problem 2 2.5 (a) Each testing of a pen has two possible outcomes: “pen is good” (g) or “pen is bad” (b). The experiment consists of testing the pens until a good pen is found. Therefore, each outcome of the experiment consists of a string of “b”s ended by a “g.” Assuming that each tested pen is not put back in the drawer, the sample space S g, bg, bbg, bbbg = lq . 2.5 (b) In this case, we simply record the number of pens that have been tested. Therefore, S 1 ,2 ,3 ,4 = . 2.5 (c) In this case, S gg, bgg, gbg, bbgg, bgbg, gbbg, bbbgg, bbgbg, bgbbg, gbbbg = 2.5 (d) S 2 ,5 = Problem 3 2.9 A5 , =• bg lifetime is greater than 5 B7 , lifetime is greater than 7 C0 , 3 = lifetime is not greater than 3 AB 7 , «= • lifetime is greater than 5 and 7 AC «= lifetime is greater than 5 and not greater than 3 AB 5 , »= • lifetime is greater than 5 or 7
Background image of page 2
3 Problem 4 2.13 (a) AB C A BC A B C cc c c «« » « « » di 2.13 (b) ABC AB C A BC ccc «« » « « » «« 2.13 (c) »» 2.13 (d) The events in b above A B C bg ns »« « 2.13 (e) Problem 5 2.18 Since the event a,c lq can be decomposed into two mutually exclusive events: a and c , f= + = Pa , c Pc 5 / 8 l q l q Similarly Pb , c 7 / 8 l q l q =+=
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.

This note was uploaded on 11/29/2009 for the course EE 131A taught by Professor Lorenzelli during the Fall '08 term at UCLA.

Page1 / 11

part3 - ECE 863 Analysis of Stochastic Systems Fall 2001...

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