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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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