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mt2-solutions

# mt2-solutions - Date Time 17:30-19:20 Instructor Dilek...

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Unformatted text preview: Date: July 16, 2009 Time: 17:30-19:20 Instructor: Dilek Gt’wenc INIP ORTANT 1 Check that there at 5 q testions in your booklet 2 Do NOT use your ob. 1e await calcula 1'. Turn it off during the exam. 3 Show all your work. ,pm results witho t sufﬁcient explanation and correct notation might not get full credit. Write your name on ea 1 page. GOOD LUCK! vulva-nun IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII u nnnnnn 1. Balls are randomly withdrawn, one at a time without replacement, from a box that initially has N white and ﬂat black balls. Find the probability that 11 White balls are drawn before In black balls (N 33 n , WIS m).- ‘7'0 ’PLWC 0 ﬂ WA}%€ 550/15 WIW \$3.. W/yléc/rawkgu _/9 are. a 71075»! 0 m é/ac,.é_ 641/5 7 and or)? 'y I,” a care, OWL «CaaSiL /) (Ax/Hide. 5M5 /’/1 #4:. //k§7£ n+mw/ WIV'AC/meWLS- 44]“ X M 717/14: 99“ (MA/Xe... 5695/5 amando ﬂu, /xh~/" ﬂ+mm_/ Wx’Ma/rawn bMSJXPZAbn/éﬂg/fwmﬂ’h (”7.414) mammal) M) n+mmi (Q{)(e+\${*:§>- ”(Xan)ﬁ 3;; wwwwmwwmwrer NAME : .......................... 2. The length of time (in hours) that a rechargeable calculator battery will hold its charge is a random variable. Assume that this random variable has a Weibull distribution with parameters a : 0.01 and B = .. :1) Find the mean and variance for this random variable. (5 points) b) What is the reliability function for this random variable? (5 points) c) In a random sample of 50 such batteries, approximate the probability that more than half of them will hold its charge at least 12 hours. (10 points) -—(0,0/)X2“ 100\$ {002)Xﬁ X30 0) £00: (/40? Fmt-ggﬁ ngé) .3: Sign: g‘gé ADV/LS, Waxy (#10) {rm 3%.)» [P Maui-Hi —-.= /00 (FEE) “'(igF-Yl — /00 (/Wonags):€00)@,m\$)e 2A5 5—. .4 UK is) KOOZPKX>5>\$ é/MOZVC 00 0/” 00 “(0,0076 : ééIOOIDX1mL: Q «ma/NZ" ﬁg): 8 away/z)?“ ,4! m. , W 3 20,23? 0) /: P(X>/2’>: £02)? y' 744 (9/ (goat/(Ionics 50H JAM” CA“? 0% (“13/ /Z 49"“ I'II 30 MM W WW WW2) ”Pr/Its W W7? 1 y\$)(0.763 :. 30/ P( y>25> W/QKVeM) WP(Z~,>26“O'“”“ :WZ> * 53> 30( NAME: .......................... 3. Suppose that demand on a given product, during a given day X, has a Poisson distribution so that P(X : 0) = P(X =1). a) If a merchant stocks 2 units of the product, what is the probabiiity that demand will exceed the supply? b) How many units shouid the merchant stock if he wishes the probability that demand will exceed X’V Déiirrctnq/ /V ﬂJ/kxaﬁ {/1 ) the supply to be at most 0.01? —-//> f4 0 . a 27 ﬂ ( X? O) :5 ,é-.57/¢M :17 W K X 11/) : wwﬂ‘lngwm M) Maﬂﬁ-‘z (i H T; 3 ﬂ: '5') X Iv ﬂaiifean {#15 /) Ox) p(X>2):_ /——pCXé2«) :/-—*ﬂ(x5o>m mekwxol) 1’ / ”'g/wigmlmwzﬂc? l9) 613' #usy’ «inf/.5 1%; mg,“ a s/ie/t/ C? ﬁ’ﬂ‘MJ’gy .ﬂ(xw/.>a»/)£ ﬂow/g. 41. 1,. 5) gnu/0 ”i ../«—€1£'“"wi€ ' 2 Act/77L ,5749gé_ ﬁxw/ @m/ awe/LLWK/Yw/é 1/010) '2 /00 27:) aw] X . MW}? £Xac7£ @‘g’rzd/Vb/I (ﬂl’rSJ‘a/I) I 7‘ at,_ ﬂ J at)4a0/ A? all/Mi we /mo/ SMMS (X>. ., , in ”:69, z 9(x>2)w has /(X>3):0,0§r.m e 0 / w x ”I w 0,02,.»- / e 3: (7,00% thw) 24 as /_'s 4, (gal?) 4. It can be assumed that human body temperatures are normally distributed with a mean of 36.5 0C and a standard deviation 0f0.39 0C. a) A certain hospital uses 37.6 0C as the lowest temperature considered to be a fewer. What percentage of normal and healthy people would be considered to have a fewer? Does this percentage suggest that a cut of 37.6 0C is appropriate? b) Physicians want to select a minimum temperature for requiring further medical tests. What should that temperature be, if we want only 5% of healthy people to exceed it? X: A“? rem/MAM N/l/(M= 36.5. F: 0,33) .ém-TMS .,.. , z ._ . M)P(X>3?.6):P(Z>W)r’0(3>2”32’) /F/”z) ; /.. 0,39% .2. 0,0024 Yas. f/ farm/7 Li ﬂew/£3 156a f/mémj Oémx’zlyo fmﬂgalvﬂebd >396 1'3 «rm/y 0,2 ‘70. WAM #143 Ana/rem, «a- S 0 Serum /’7‘ SAW/J Ag, mﬂW'QZMoQI as few/2f. lo) ppm X...) .3 0,03 _ XDW?6‘5 :0,05’ Pt2> ma ) W0» 2;) a x...“ /9(aaas) w Wilma) : 0.05 m) FKZDDS 0,35 2) 20\$ L643". 3:) x0 5.» 36.5 aw (o.39)(4645) 2:: 2?. g E 12%.. . .. 5;? m '1awauT-P-wwaWag—(nawéruowwj.<xWM‘QA,‘ NAME: .................... 5. A man and a woman decide to meet at a certain restaurant about 12:30 RM. If the man arrives at a time uniformly distributed between 12:15-12:35 and if woman independently arrives at a time uniformiy distributed between 12:30 and 1 RM, , a) ﬁnd the probabiiity that the ﬁrst to arrive waits no longer than 5 minutes. . (16 points) E b) What is the covariance between the arrival times of the man and woman? 1 (4 points) / X x. 6 X r amt/tr Mm (j) “WW" 6 30 / .5 /5 / A 3 S In Cab/1 d 1’ (7) 2 0 U / 4 _ 30 ﬁx 4. 6 0 IS 41 3°S‘ (5 o o I :1 =ff ”"W “(‘6 ‘4'" W—"S‘ Mo L3.— —-5 4 ”(—7 {4 5 ~P<I>< >445):- W 5“ 7’45) 35‘ +5 5 .___/., f 600 dKQ/Ej .25 30 x 3‘s "t" W“ o s 600 f {a 2 >913 525 s i... mm - _.-4._._r__m.MM_L_MWWme k 2 600 (Ag-N“ _25Ia>2LQ f 30 35 4o 1,; “EJMé it % ﬂ / m )(25 ._ { 600 2. 2625 > 251““? 600'2 z: / _2s I: ml.“ moo (35 ) A2, I?) CJV(K’Y) \$0 '9 AﬂC“tV5-’€' X CW“! Y ﬁfe. Ibqi/t’f-Mtwﬁii ...
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mt2-solutions - Date Time 17:30-19:20 Instructor Dilek...

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