hw2b - / 1. Five cars start out on a cross-country race....

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Unformatted text preview: / 1. 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 . What is the probability that at least 3 cars finish the race? 2. We have two dice, A and 8. Die A has 4 Red and 2 White faces and Die B has 2,Red and 4 White faces. We will play a game by first choosing a die; die A is selected with probability p. The chosen die is tossed until a White face appears, at which time the game is ended. . After playing the game a great many times, it is observed that the probability that a game ends in exactly 3 tosses of the selected die is 7/81. Determine the value of p. 3. A biased coin has a probability p of coming up Heads when tossed. It is tossed 6 times by your friend who tells you that Heads turned up in more than half of the tosses. Given that information. what is the probability that Heads appeared in all 6 of the tosses? 4. In the figure below, the notation __4J___ represents a communication link. Link failures are indepen ent, and each link has a probability of 0.5 of being out of service. Towns A and B 'can communicate as long as they are connected by at least one communication path which contains only in-service links. In an efficient manner, determine the probability that A and B can communicate. 5. A pair of four-sided dice is thrown once. Each.die has faces labeled 1,2,3,and 4. The discrete random variable X is defined ‘to be the product of the down-face values. Determine the conditional variance of x‘ given that the sum of the down-face values is greater than the product of the down-face values. ./é. A computer will fail in its kth month of use with probability —l " J. 4 - ' ~§ Pk " 6- : “1.13, ' . J Four computers are life-tested simultaneously. Find ' the probability that: a) None of the four computers fails during its first month of use. b) Exactly two computers have failed by the end of the third month. c) Exactly one'computer fails during each of the first three months. d) Exactly one computer has failed by the end of the second month, and exactly two computers are still working at 7. a) A wheel of fortune is spun three times. What is the probability that none of the resulting spins is within 30 degrees of any other spin? b) What is the smallest number of spins for which the probability that at least one other reading is within plus or minus 30 degrees of the first reading is at least 0.9 ? ’//E.The probability that a store will have exactly k customers on any given day is fit \123 ‘é- (€g3 ‘2‘“°:U b‘“ On each day when the store has had at least one customer, one of the sales slips is selected at random and a door prize is mailed to the corresponding customer. (Each sales slip corresponds to a unique customer, and each customer buys exactly one item). a) What is the probability that a customer selected randomly from the population of all customers will win a door prize? b) Given a customer who has won a door prize, what is the probability that he was in the store on a day when it had exactly K‘customers? P=oQ 9.: I-P = ( pmbabfl-‘w H'Ia’r ; 4;.- bveak down ) 0.8 W pmabmw #13" 1+ hawk 5 cars finish «he ma. :5 When WHQn 3 the die 1 ex A as selected 8 :s SMELWJ P- (g)? ‘§ Prnbabzmu a: Heads appeared + (up) (-9 4. hnws :5 (g) 185 0.22 + 01‘ 0.2' + 0%" 031° = 0.94203 Prbbublh‘q at mm tau: :s % probabluq ac r04 tau: :5 2; 0 Phbabucn‘ cc WM‘M Cau: 3% 3.3 pmhabzmq 0(- Ma cm :5 .16. 1 p: our) .L 6 (2) P‘ u-p): 6 5 1’?sz 15 p; ("P)‘ 6 hmu is (b) 9‘ (“no 6 P( Hands apocaué (a hm“ \ Heads append > 3 fimes 3 II ( p6 4 <‘) PHI-m1 . (2) 95m») « <--?\° Lu P; be Hm pmbabn-eq 0C our 0"; Sauna. The Drabdequ H13? a and b can wmmumcan is p(°‘)b) = l'p\P’l Pa “mt pnbahzlnq #13? c and 0‘ can Lomnluniafl ‘IS pecan s (1-p.)<‘-9,)-. 0-9..) ____~H____~_ _ _ 5 '1 P(1.1)-| (J5) =§ P(3.L\ = |-k‘_)2= 3. ’1- 4- 3 5 p(5.l.\ = l.— = _ '2 ‘- g Mam» = u- -3 = L' '2 H 8) I swan = 51 L‘ - "q 8 ‘6 ‘ 1'29, p(A.m = I '1'? 205 b." 1. 1nd I; bg has and» “rial-hrs ca. +1“: pair a: d-‘ci and X : 1.x, T: x‘*xl ; 10.11 1 6‘ = ‘HR omd;h'ona\ Vin‘nmz cc ‘11 4 ' '3 .-"‘2. /{b - q‘wln .Y Sum/hand- :> M 1:! x ‘r 1 = '4: P C X '1 | T 3 = V1 p E 1 = 3 I ‘q' j . 1/” P [ x .t \ ‘r 3 ‘ 1/” fl EC1°IY3 = :7 PEI‘IIY]+'I‘ pcx-zw:~a’ $417st: ‘4‘961a4w‘1 = .L . 9 ‘E .11 ‘23 nn‘q'}=n 1 ‘2 ECX‘lY]: l‘~*o 'z‘-;.l-o 3‘ 5» 4‘3}: am; ’2 a“: straw] - atrium : ‘°" 53 = Lee 4: 11950 '1 m - - ah pmbakm: A Lomyu't’ w-H ran m .H k‘“ l‘l‘an‘H“ 0“ U“ W “l p '. 1; 5" L: L13. 5 s 5 (7) Lu E~ Myanmar m ewm *3? #5: L?” wn'pu‘“ *0“ (all at HM 5m manvh ‘1' uheré i "~2'3"‘ 33‘ 4 a L \‘ in) P‘Ecx) ‘-'- %(§) 1 5 ‘~-|-1.’:.4 P<Ecl)= "15:: ;,,_13.4 ‘7 d The Mam, a: no“ ac me 4'" ump‘frrs Caals dung SM.- warm: as my 75 N E” n E1. n é,. nay) = NE.) 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F be the cum Hm uuuw ma umutm are mu mm”; u- (N amt .c me am. nus-«h, “EN” = NHF) NF) 2 = mm m)u—'ggu%) ' whee El 5: means smut-bu. one “Inpuflr “a ‘13.“ MM“ an: 1“ ‘9“ MW.“ p(E.‘F‘ 3 [P( 569‘ ‘ Had] I l-(P(En\¢P(E¢4) 32 =(?)5‘%"-%'\‘s>"a1h-«QVéwéfién? "= m «15%» (Ls—‘3 a N“ [Pm-n. 9mm fl-(Piic-NP(£.1)] L ‘1' ' '3 4 e5 (f)[5‘§5]["(§‘%581 =(f)-u,, ‘15 45 m‘. Lu SI 9;. 3M 95 5'! HM: film pud’hm; *5 be Mum" d ‘Tfie Wuhan-q Cat 3 9pm new. we haw: ihm use; +0 uncder a; Hm spin. nu M glzo and A :s 22 = $3 ’1“ 'lfi' u I; S$é(§.§) Wm 55E(91;y:,‘_‘zu) $.15 7% {in P-- 2:: 22: 59% I“ 1'“ 5. _ a an L5 (545‘8) “1 ‘T 5. -l". 7. “Rn Sgé (T, 3!! 6 ) %-§W : 1' fig d9; 1‘ '1“ 1.“ ' ' 38-3 fi 3- “m 956(‘5 St'E)U($-n%.*fl’\ _ n =I‘ HEW—9* V" T ' 91'; j ‘Thz Mafiaqu mut- none“: ON mun-q 5pm; .s «mm 30' a: an oak» Spin K P p. p :1 .'.'L 1 . 1 ' ’ "P‘ 1% me 4 Is an 'rhz Phkbilum um:- m ’Zrd sin is on 0(- no “M gar on .s 5‘. 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This note was uploaded on 01/05/2010 for the course ECE 01 taught by Professor All during the Spring '09 term at Aarhus Universitet.

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hw2b - / 1. Five cars start out on a cross-country race....

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