EE351KExam _1SolnFall2007 - A Problem 1 i T Sea-whims EXAML...

Unformatted text preview: A - Problem. 1 i ' T Sea-whims) EXAML EEask mt 1004-1 Consider the following thieg c_v__e_nts A, _,B C, where '- P(AanC)= 0.,25 P(AnCnB)= 0.05 P(A)= 0.5, P(B)= 0.5, P(AnB) 0.10 Find .= . .(a) £040 B.) faCb)..-P(AmB) (c): P(AuB) - (d), P(COE lBuAl-u- " (e) 19(5an IA)? (@5323; PC chglE (3;); P (_ CcmflnLBuM) ._.._,._- (6.2. P(anlAB— P ((205 ' P(A) M... \/ ”— (9’. 15 -: H - Problem. 2 . ' ‘ Consider an urn with hfltwo white, and two blue marbles. You randomly draw the marbles out one by one and note . their color (you do not I ace the . bles once they are drawn). Calculate the probability that you draw them out in the following order. red, white’rred, white blue / :1 Mme. Pé RAD-7. m3 Q4305 343' : mm H with rm New R} Mug P ( @ng (howl A135) 3‘ P L B—S—i , Rea—Wm—Afiflrfl-Qfis"E(“VJ-b-i—Ri—A'w'7:Q‘B$*D“-g+‘Q-w£—)—“ (538 mm;- 2: :43 [email protected]_ ”i “ ‘” iP(Q‘nwLnls3nQ‘ths-‘fll5é\:(—=00mi,‘ Ce- Mme—‘3: 32; ‘WW I> i ”finrjg lllllll _ - @@ ’ ' L to EX$X3M2M0;— : 0,0in coco . 90 F‘ PlJ‘ Z > '2 v——- _ (fie? \usbm‘nwg .4” % P[[)\‘\’~\R(HWL(\B_9)>2 J5 (@E '\>(w5\R (m; r\\33 0R9 C832 \3‘.C1$/,\Rmui7_0135(\|(l4_(\w_gy:—i 2/5 » Problem. 3 Consider a digital data transmission system which is designed’to transmit only three symbols X,Y, and Z. Each of the three . symbols is equally likely to be transmitted. Due to noise in the system, if one of the three signals is transmitted, the probability of the receiver correctly detecting the symbol transmitted 1s 0 88. In other words, if one of the three symbols 13 transmitted, the probability of the detector at the receiver incorrectly detecting one of. the other two symbols (and thus introducing an error) 1S 0.12. (f , (a) If symbol Z is detected at the receiver, what is. the probability that symbol Z was actually transmitted ? (b) If symbol X is detected at the receiver, what is the probability that symbol Y was actually transmitted ? 2-4: 1—-L—"~”J 2‘4:- Mamie. +PcAMS—Lu-L42-l-za29- —s‘—1—M—‘°°\3‘I . - WM _ Y u P (3:12 Pug: Wag :. g _ games-1:4: 22> Jrrcwmktm W ' - swam-mt ak=> debt/9m? Wei 3 _ . C&)QU1L+1‘0.M [15 P Lilli-1y) _.._ Saw \ale W 11% am know ~111ch PC Erad2t3= 0 8*)" 1911-24 {XE\—\>(EA\1-Q 20.172 13M“: Watleafl: P {£91122} WES 5 , _ 1>(m12e1:) 9121+ eta—3.13:9 P0799 +1 was?“ 11ch Pug 2' (a MEL-g \ ... (peel c ‘9.) +£a1z§té\ +ta.\L.3_1'/a\ 1 i 0' 2‘? V . .2: 0"” 20.73% i a.e%+o.\1 +~¢°:\7— ' 1W L53 W31 X a\ = Mttie m“ _______ \(XM‘LHPMQ + Hmmgwflx +— Hawggp 2g : (0.113(33 . . . Q3017.) (a) 14(v«.121(§\+5(_0.8*§\l%\ 3 0. 12. 1 M~~~~-~2-M~ = 2‘9“ _L. :. 0.10:1- 1 [a 12~§~t~(0.1>_)[email protected] 8%“111'1' ' . . ' l \1 (1131213: 0.102% W a a , . V. fits. ‘1'A(),.\c_aa=-LLaci bu +h¢, ngpuerkgfl 0M“). 43:3"? J34“... -l..¢c;..£c2(AA $41101??ch ‘L‘lrtcwzek 1 "Emma CL;L.Q.‘9 hack a .9; "“— P(%E\Et,§2 5 M g " '5 = L013 (we) (GM-L0 oé)¢'[email protected](>31 ’ PCELHKOU— cw emf/51 ' o 063 l 2- W — -—2 CD'OQN 93 "—1—-(@'0Q_"§C 34 (0 312’“ a; 3/5 Problem. 4 Consider the following diagram of a system, where the various subsystems are represented by‘ ‘switches”. Assume all subsystems operate independently Furthermore, assume each subsystem operates properly with probability 0.8. Calculate the probability of the overall system operating properly. ‘ N 0'06 \3 . /"___..' / ' a we é~—___/ an. *0 == *i I l‘ '“ = L.!‘ ......———l 0(‘7IL9 P(E\:Oflnb+0l°l(9“ (Ute-((931,: >’ Problem. 5 ‘ The managers of a computer store near campus know that when a student walks in alone, they make a sale 5% of the time. When a parent walks in alone, they make a sale 15% of the time. However, when a student and a parent walk in together, they make a sale of 30% of the time. When the door to the store opens, 40% of the time a student enters, either alone or with a parent; and 90% of the time a parent enters, either alone or with a student. Define the relevant events as follows : S (student walks in), P (parent walks in), and C (a computer is sold). For each time the door opens, calculate the probability that a computer will be sold. 3 ,. — _. ~ I ._ __ ’ {ax \. «C (_._ \E/l P.) —~ .01 (IQ—b ‘ - . S P :1; i Clo-3 P—c at 39 P >—« c». '-'>. g ~ 3 ' _ (ax P Cchg’mPS ?- 0'3“) i 5; a (ex) ?(35 : 0,40- 03) 'P (P5: {9.50 I“ M‘fliflj’ swap (£3400. Mime. Lomaiflntoumi nonhumwxwu vao\vima_ eegwi: C (on wuotwwtu" M. Sold” To QVCL\U_C_LJ'(‘Q.. PC¢\) our; Muzak Jrcz) cm EX'QPLkfiil/lfl', Nana) Pt§n m) Ma P420?) ~ 1 : mMro +ar‘bo ___\D(gm>). So Ptsn93=efla A 9 we’re. Put-‘49); -.,\>1(_,.Pgn;.g\+Y-’($fl§\ PCS}; P( $053+— ?Cs 0P}. (0,610 = 0,3 +PCP-(L?) 594—0: P(S(T«E.>’r—0r3 Pi\3fl:\:0.°10a,g.3c9#07441. . PC snS}: 0,4co-eo‘30: Osk PC saw: at [ - W Fm. Lawn? Tat-bk \Bmmmwuk PCPmEB‘faL. PC“ '5 ”9‘3”“ W30 $34 9 (Mgflm 9650-93 +- PCLJ an 93 -\>(s./\P) 1 :. (0:05:5(ouu +(OHSK0. (93 +(01303gggg \PfeB ::. (miss? 5/5 ”9(30931‘ 3 FNSUFB: PC‘Q‘HNFX _‘ @(SAP) i=>'\3(Sfl\3>:i0ua-xqio'}°i~t rotf ...
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