Lecture 2 Notes - Tm 17w v M LW KMM ‘ wagiw [email protected] 2‘...

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Unformatted text preview: Tm 17w v M +LW KMM ‘ wagiw ) 5mm! @me 2‘) EXQWPW (AL m» mfimfim fl; Vamwu Sgamg (pzéj Emu/mpg 2 3 - (WEI/fig m0 WWW (Paw) S‘ (21ng m spa UL : 4%. w( M [1m E; WWI $Mw 10 3 (31 fl UKUEQV Vpalfi (m 5;» OUC‘VLQW 14? MW {@Wfifi KW (79 0t H EQQSMCW/(SLQ £3 bah/374mg»; CA&QWGtEd @W] S” @«“ xg K Avai) Jf 5 6'1 C D! [ REF/m o F ' (303315 (,2 Gmfimwm/Q L Ch MW [10 [34/] fl / E), C j Adi W" CflQW/LO [ENE/i” B / fl §mbwj QQ g‘ 5mm qflj W (i C‘ N? “m w: t G‘VW 05F s: w? m, oi‘afim M QM WI ‘4; 0? a mi? 9M}(WM4“1 % ‘ ' ” Mth (91;? WWW" (“0143/ (jmé‘aL ; (Lu/I % g: WHAT IS THE SAMPLE SPACE? WHAT IS THE EVENT OF INTEREST? Problem 8. BOOK , You are designing a packet voice transmission system. A speech signal is segmented into 10 ms chunks, and sent in packets. However; to save bandwidth/ the signal is only packetized when the Speaker is NOT silent. If you have a group of N speakers in difierent conversations, chances are not all of them will be speaking at once. You design your system to handle up to 8 simultaneous speakers. HOW many calls can you admit into your system, and ensure that you exceed capacity no more than 1% of the time? , i / {fit/£64”? ‘ , Z )0 ll 12 i ”it Sly \ = g 5:» 0’, / / ‘ fl ’“ / J / 2 , “l A “W P’ :2 0U [0/ H/ g ‘ekvceédz capacia], ‘ mm mom Wm M 8 rpm/1m ‘ ‘ H “(‘8 thhm '15 iglcfiaivwlemi/ WraMWa/Lflificm/éc/J _Nul-€l 4tmo PVOWSlW” fl} imam] oil/\B'V’S‘, HULK} “ma Ml PCS. WHAT IS THE SAMPLE SPACE? WHAT IS THE EVENT OF INTEREST? Problem 11. (PROBLEM SETUP IS FROM EXAM 2, FALL 2015) Five cars start out on a cross-country race. The probability that a car breaks down and drops out of the race is 0.2. Cars break down independently of each other. (a) What is the probability that exactly two cars finish the race? (b) What is the probability that at most two cars finish the race? (0) What is the probability that at least three cars finish the race? 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(xi/Lu, gm, Wig/5m Md mM/xplfmflw/f ‘ mm {Jame/MW % din/V1071 only £ WW {JQ CUM W pwwm’ W; Comm ML a b" W77 , aSSbc-a‘m/w/‘thj 2 and O/m/WfimbyQQ fly 5%} Wflimxé , CWMLM/fifl A Ué Z 5W} AWE: 50/) mod mm A UWc) (A W) W Wig/16) 1W5)“ 'Dt‘dh‘lmfivt Pr U (lg/K) :(QrUQJfl (HUQ 0M Hfl (1%ch :mfl@>U (Me) Mmc‘tyu OMd {\flkfikcfi/Mfi Com H wafed f0” Om arBaJfi/m' *1: d2 5&7 l/\ U A; r A‘ 0/11 D with «Six 0/ WA (\LA'JLSLi/Llfa 13:02 42135 OLA: "- AL UHLU : Lil X’D Q6 {1/} (“E/0v; l [GR/t4); 14m 0m mwfméfi Jag—Lam W ‘5 flrfflfl-L T C!) 7QV ch47 673/3 {xi/Wm / 6/3 "t )/ ”ATV/A77 “‘xA'“ OWL eve/tedflmuq €2<WM57LH~Q {fl 'm————-—""‘/_- ht A, ,A;) M/4n OWQ/ MAM/Mali? €KC/M/jy;% WALL MLu‘flMb exbxaM/T/W/ W HUM >Z 7 jfiwm Ck Wk 1 MM 92 3 TM» WWW W PW w; W ‘J‘hmwlwh WM mflfim .m , A Wm] WM M 2le (X) fiebem I}; weed De m DY?) 0M3 Lea/VJ 9C8 )/ whfie/L’e WWI/157% : Cam/V Le WW1- b/ we Mae/CW /. axe/LA muffin. We feyexeeefi’vlkaete Mex/{,9 / field fimDZe Q, mm ; VQW’I ”ii/Lil dwjgyamo _, _ A A e ECE 302: Probabilistic Methods in Electrical and Computer Engineering Fall 29w: 2:» r '7 PURDUE Instructor: Prof. A. R. Reibman U N I V L R S I T Y In—class problems Fall 33:6 219W ‘ (August 3% %) ’lwo ab 69 L4 262917 6 gf‘dég‘ [WEEKS SPrECl'G‘ed) we die Exercise 1 . Roll 2 dice and observe the pair of the number on the first die and the number on the second die. Let A1 2 {doubles} and A2 : {the sum of the two numbers is 6}. Sketch the sample space, and A1 and A2. How many outcomes are in A1 U A2? 5 : gm») 5 #79346] j Mvfil/Cl' A 2, 2/ j'é, 71— A5? (Will/'1), (3,3), - Wilt/)Jéfijflé/(O; Exercise 4. (FROM HOMEWORK DUE FRIDAY) For each of the following relations, determine which is valid for arbitrary events A, B, and 0. (Note: to be true “for arbitrary events”, it must be true for any such event. Use a Venn diagram if it is helpful.) (On the exam, this was a True / False question. For this homework, show whether it is true or false.) (AUBVUC)C=IACUBCUCC (AflB) U(AflBC) U (ACflB) = (ACDBC)C (A—B)—C::A—(B—C’). ( AUB)fl(A-CLJBC)=(AnBC)LJ(AcflB)LJ(ACflBflOC) ...
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