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# mt2 - — £55.5sz COPY" Date Time 18:00-20:00...

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Unformatted text preview: — £55.5sz COPY " Date: November 28, 2008 Time: 18:00-20:00 Instructor: Dilek Gﬁvenc ,/ . ,/ IMPORTANT 1 Check that there are i question in your oklet I 2 Do NOT use your mobile phone a c culat ' . Turn it off during the exam. 3 Show all your work. Correct result thou sufﬁcient explanation and correct notation might not get full credit. i I 4 Write your name on each page. -!---- GOOD LUCK! uuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu 1. Assume that the probability of error-free transmission of a message over a communication channel is 0.95. If a message is not transmitted correctly, a retransmission is initiated. This procedure is repeated until a correct transmission occurs. Assuming that successive transmissions are independent, What is the probability that exactly eight retransmissions are required to have the third correct transmission? (Deﬁne the random variable of the question and solve) X.’ # 4% TL/GL’U'M/ES/b/g; ﬂair/(J’LQ/ 74: [tout/1; #6 gr/c! Cal/{cf gLru—Ivs n’U'SS/iﬁﬂ- X/v Nap. gm (/23 1 ﬂ: 0.35) f/al/aﬂrmizmms + 3 Let/”“1 ﬁrwrmrinlon: -= fl fifw'r'frvwirrizﬂg 1000:“): KEG/Olasfmoﬁg N 0 {/ISX/0f9> 0%....— NAME: .......................... 2. A system with three independent components works correctly if at least one functions properly. Failure times of components are exponential with means of 10 000, 20 000 and 40 000 hours, respectively. Determine the probability that system will work for 1000 hours. X2"/0~1W4 94m; elf Hm. Zma/ mnjfwmil— X7. ' / 2.0 000 , 9.0000 (x r. 6. i (X2) 3 J L) 4 500 X33 dafL/L yjam 0?] (14‘; 3)me Lam/0:33:41!- £(X33Z40000 :9 %()§): / a 40000 40 (5’0 :3 AW o X: 7% 62% wm‘pamﬁ {/wrc-Ab/r ﬂnyzrﬁy at! (Wt-50‘ AM,“ [k 3. ﬁsﬂrys/m my MA 34" Mate/twrs) :P(x2/)s/J(X=o) /9(X=0) : POQL/wa) 40(X14M00)‘ ﬂ(X34/0¢9c9) MW _,2<_r__ F752; p(>(/4/000 )ZO/m a /0900 0/4: /—- 6 H200 , X2 ”215, p()(2’é [00(3): f / é, 200906;)(1: til-‘6 0 20000 / X3 ‘FF ”(X34 /(900 t ”00/ “, go r , = /- > of éaaoo 6 ,0000 0/03 e -1. -——i~ *1- : /__ (0,095)(a,04§)(0,025): 5,9?38 N I a) NAME: .......................... 3. Suppose that demand on a given product, during a given day X, has a Poisson distribution so that P(X = O) = P(X =1) . a) If a merchant stocks 2 units of the product, what is the probability that demand will exceed the supply? b) How many units should the merchant stock if he wishes the probability that demand will exceed the supply to be at most 0.01? X’V Dimwo‘m/ /‘/ /%rjr.raﬁ (ﬂ) 2 _—_ /-—/9(Xé2_) Q) p€X> 3 ,9(,Y:o)-—/90(=')FP(X=Z) ":aHQg? :/-* 2)axyu7um% Mcmumwﬁ ya; Kﬁ# ﬁ=l V5257 6/3656?de [.5 gift/M's dﬂ '4)ép(X~/2.Q-/)7Lﬂ(/Y_/é_(/Q_l)) /9(x>a):P(X»/>a / I _> Arm éP(/X»l/%a”)52;:7gfj ‘— £Xacjl GZ/g’g’zzuréb/I (”O/\$5321) A? rib/EC WC .rha/ 5m¢lé5% ¢L_ ~/ 6 Z0102. Mex/ET ﬂows) 4— M’ ﬁ(x>2); a08 re! .. ,ozan—e :— 0/004 gnaw”? 2x, [.3 4’ (0&4) / /’(X>3) e 0/03“; NAME: .................. 4. Pmar’s Friday class starts at 10:40, but she arrives to the classroom at a time, which is unifonnly distributed over the interval 10:30 to 10:45. What is the probability that _ a ) a) she will arrive to the classroom at least 2 minutes early. ( 5 F ‘7' H b) If there are 36 students in tln's class and the arrival time of each student independently uniform over the interval 10:30 to 10:45, approximate the probability that more than half of them arrives at least 2 minutes late. {/5 f: a Mfrs ) X” ﬂag/f,— W/‘f‘r’v’af (745412.. /\/;’5 Vﬂfgﬂfm 0/: (5/ A?) a) Site. Web: arr/1:11, {/mm /0,'3o 7L0 mxgg. 27 ‘= alx :i P(X418‘) 0/ /S ’5 5) ﬁ:3r§ anunw/L Fm; 4d ex 5505M? / 0.5 for) IS ﬂ(5luo(w7£ 4,7,3,“ ml £41.25} 2' maﬁa: (sulfa): FOLSIQ) Is / .995“: 3 =—/——¢0,2. __...—— /S 5 V74 9; SAL/0124f: aural/L GUL ZeaS/— 2 ”mirage; ﬁnal I}: 36. VA/ grin (”=36} F5012) ﬂ/ﬂ:(36)(0,2>: 71,2 " M = Q:/ (/5127 yl/xc {ta/ma! a 043 01/4 W- Vi36)(0,2)[0 s) , 3,2:me (LS // F(Y>/8>:f?(ya/3)wﬂ{2>ﬂ {9 254.33; NAME: .................... 5. A particular nuclear plant releases a detectable amount of radioactive gases two times a month on the average. a) Find the probability that occurrence of the second emission will take at least 40 days. (75' W9”? ['5 J b) Suppose that waiting time between two consecutive emissions has Weibull distribution with parameters or = 0.01 and B =2. Find the . expected time between two consecutive emissions. ( 5 fag/941(3) ,}\£:H:Z 5:11 ”2.04%: 30 0/44ng . _ 2 _._/__ SDAFEE’IS Ol) X,‘ 265 96/ mir'fjfr’a/tf ! #6? g)” XN pm‘SM/l (ALA:H= é;— (x ___, LK”; Xgatgz- ~ T' Hm; 0% m Saw/ml Len/394311. 2/ 10) :: P(X£ i) ”(T / ppm?) Ham-J) t: 6 ,3. 3—4- 7” gumm°\(°£=2; ﬂzf—:/5> 1L 9‘: a” ,9 1L "5)? ”go/r ﬂ(7—2403;/___L.——ff€f’gglé:l (f6 1* a lo (/5) lg 40 4'9 as ”5% #ﬁ IOfi—QQ +(ﬂels)l x5 5; K W 2%é%+é3:é3(—g—:02§5 A) X/V UUM'éM/LZ (Dir—0,0,) ﬂZZ) ...
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