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mt 2 - m AQEJEKVE(2:926’Y QfieL-k manage Mf’T'TH.230...

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Unformatted text preview: m AQEJEKVE (2:926’Y: QfieL-k, manage? Mf’T'TH .230 Date: November 24, 2007 Time: 13:00-15:00 , Instructor: Dilek Gfivene MATH 23 IMPORTANT 1 Check that there are 5 uesti 113 in your boo Do NOT use your mob le p one as a calculator. Tu 't off during the exam. not get full credit 2 3 Show all your work. Co re results without suffic' nt explanation and correct notation might 4 Write your name on eac 5 TOTAL 20 100 GOOD LUCK! oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo 1. Let X be a Poisson random variable with parameter 11. Using Chebyshev’ s inequality find the largest value of a).P(X53), ' b) fuzzy). meo/ISSOflKfl). ECXD=fl Va/(X):H ’ so PMs-11,); Wx—M 4 —%)4 FOhMé «1g harm/19.134) :FUX- (41>. %> :9 w 1% 1411—41234»: ,1 Wm P(Xé%)4/(1x Mari); Log; ”/09 £24):- PM-Wéflkflflt MHNWXU 144-14) :mixwl> >14) :3 Ana N” t" “9“”? Wx>2fl>< *0le Xl>X>éZ/ ‘25? fiWEWfi? NAME: ...................... 2. Suppose customers arrive at a checkout counter at a rate of 2 every 1ninute,_,_ a) 'Find the mean and variance of the waiting time between successive customer arrivals. ( 5 points) ‘ I b) if 100 custorners arrive at. a checkout counter in a day approximate the probability that in more than half of the successive arrivals, waiting time will be less than a minute. (15 points) q) A522, X/ wax/31mg Am Wm guch/u wflbgfr‘ ,zx XA/M/ 0:2) ./6X)5 26 x> o 10) f:— 10(me MM Zen M7,, .1— mfluz/é) :—= Df’zc'g’xe/X =1 L- ”Mia : /P€Z: 0,376 Y} 79% % Success/vi earths/5 writ/I figs Mam ,1 mind}; ‘ [Vim-1W, at,” A, (570- cunt/ale, ngm (xi-:99 #020,“) nprsswxom 875 \1/7/97’: 35(0Iéggé'TJ/av4) , i i ”—1 3.45 fl b.4015): FCYaso)~/fi (22. 59- 0'5" 3?.) 3.93 :P(2; 45,29) A231 ‘ : 3. The time between the first and second healt attacks for a certain group of people is an exponential random variable. If 50% of those who have had a heart attack will 'have another one within the next five years, what is the probabilitythat a person who had one heart attack five years ago will not have another one in the next five years? - 74PM, Mylar/1 MA/ITSIL‘OUIJ SL002“! Aria/m4 CLilllchéJ mefl(,\) 5 ”A '. /)\€ XQZX =" r 0 '§ HEAXL 1:. £915 A Java's -5A 6 rag: PM: A: enznasg 5/]? 55 '5 rib/«74X , -—¢9'/‘/(5) _) Fl: g/Zjlée OZK: ‘6 :60?:043? 6W”, .—P(X>/olx>5> £3005) gamma/w Z? in . _ fywfl,%,) aaaaaaa _ _3, ' NAME: .................. 4. LetX be normally distributed random variable with mean 0 and variance 02 .- Find the density of Y 2 X 2 . Determine the type and the parameters of the density. erflffltoirz>J . X2 J06): / ._ e-fl 2‘7”“ 4wéx40‘9 mvzn y 1,0(_'\17{g/‘<é W) gp(xé\/g)WP(X-4~*V§) :— firefl— Iii/”“573 7 r —~ i— a /a , / ' gain. 'f‘ / a 29x1] t?! FY27} V‘Wfi U— "3‘31 a. is; th. 2"“ ”“ aka—3' Wt 4M f” 65%;?- mm _, , 1 7t EFF $4 Mich #J—w—JW'f‘w ‘02, a WP New? ' . -2041 ) yn/ awn/tax (”Li—[2”. ’J/gf > ”ff—‘6 REEEERW? 9\“U~1" NAME: .................... Stores A and B, which belong to the same owner, 2116 located 1n two diffeient towns. If the probability density function of the weekly profit of each store, in thousands of dollars, is given by x — l< < 3 for=4 x 0 otherwise 1 . and the profit of One store is'independent of the other, what is the probability that next week one store makes at least 500 dollars more than the other store? ' X; Wag, flay/an SAW. A v; W26 ”aways/mg cits ma! fl/péqérd/‘ia: fl()<> y+.L)+/(y>x+_L) t 2P(X>Y+i) n : [22} 144., 11-0343 Md Yet/u— mlwth (#293) 1/0 OHWMLK (X nex'e ' '2/0(X>W—?é) :flxéi #546” 5 l : 2 /i[(:el>fizldx Z t L 4 a: L 2; a 3 2 ' =:fi2/0&—3§%>¢X ' ‘3: I 3 ‘2. 3) 5'49 4,359,321.) :1 :71; 3—57 s 3' 3 mu, 3: 40,54 _.—-———-—--—‘"""'"'o 9‘ 'aaeanaa -‘S— ...
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