This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: STAT 333 Quiz #4 Nov. 10, 2009 4:35 — 5:20 pm Name: S I.D:
UWUserid: Mark / 20 1. Laurel and Hardy enter a bank simultaneously — Laurel to make a withdrawal and
Hardy to purchase some mutual funds. Suppose the amount of time it takes to make
a withdrawal is exponentially distributed with a mean of 10 minutes, and the amount
of time required to purchase mutual funds is exponentially distributed with a mean
of 25 minutes. Suppose that Laurel and Hardy are each served by independent tellers
immediately upon entering the bank. [3] (a) 80% of the time, the time it takes to make a withdrawal will be at least how many
minutes? Let X a’zno7Lﬁ 19m /eU7L/1 070 19m; ‘7‘?) make. a wiviéalmwal ~x/o 7778b) X’VEx/Danah'l'l'a/[21 ,l/Io) an/ 30 = e ) X7/0
VVC 7‘a JelLerm/‘ne f Sue/7 ﬁa‘l‘" = c— /”’= 0.8
“f/a = /n 0.?
14:. 405702;: 223/ 777’“; 5* ﬂuke: .aIIL’casf‘ $237 mini:ch +0 make a wh‘ﬁc/rawa/ (3’0 % a7°7i$e7ihra [3] (b) What is the probability that Hardy ﬁnishes service before Laurel? Let Y c/emﬁ 7%; Anjﬂ 070 19mg 7Lb/ourcﬁase mu+ua/ #um/s.
7—5217) Y” Byonerﬂ‘ia/Q = [/25) .
Ms / FKHm—é, 'Fl'nislies 527%]! Laure/) m =§/2—+‘/“ = $—‘ [3] (c) On average, how long does it take for the ﬁrst service to finish? Ad T ale”°7Le 7916 film: 760 2972 #irs't" service camF/e'h‘on.
7291/, 7—: min Yffvaronen’fial (7% + 254: i126 = 33%,) 777415, 7/,50 = $71.2 7/43 mindfu I [3] (d) It is observed that after 7 minutes Laurel is still being served by his teller. What
is the probability that Laurel’s service time will be at most 13 minutes long? We Wis/r +0 a/a7l'ermine. /D(X\</3/X>7) = F(X\< 7+é/X>7) =fCX\<é)é/IﬁeMeMo es:
frof rb/
=/__ej6/Io =/ _ 8—0.6 1’ O. ‘7‘5/2 2. For a branching process having X0 = 1, ‘calculate the probability that the population
will eventually die out when the number of offspring (produced by any one individual)
has probability distribution given by: [4] (a) P0 = 2/5, P1: 3/10, P2 = 1/5, P3 = 1/10 3 Fills‘t‘) We aka/ﬁe”: = CI)(%)+ (z)(’/5)+(3)(%,)
= / (Since/AS //~ We. can COHC/uJe 7424+ 770—: [4] (b) P0 = 1/8, P1 = 3/8, P2 = 3/8, P3 = 1/8 3
Firsf, we ca/cuéﬂl'd/u: =C/)(%)I—(Z)[3/g)I—(3)(%)= 77/ Slncf/M 7 l) 77; i5 'ﬂiedsmé//es+ F03l+ive 50/u7LI.0n $795649 in = g, 773/; 4 V
77;: %+ %77°+%7/22‘+ %7[3
7234—3732—5773 +/ =0
(770—1)sz4— 47/34) =0 TE=I —Z:\/5—
_/4_N_0. . : ;cFarmuld~, owinea) vfa $uaolrn
77m, We see 7974+ 770 =— ~2+1f§ 2 0.236. STAT 333 Quiz #4 Nov. 16, 2009 4:35 — 5:20 pm Name: S LD:
UWUserid: Mark / 20 1. Thelma and Louise enter a bank simultaneously ~ Thelma to make a withdrawal and
Louise to purchase some mutual funds. Suppose the amount of time it takes to make
a withdrawal is exponentially distributed with a mean of 8 minutes, and the amount
of time required to purchase mutual funds is exponentially distributed with a mean of
18 minutes. Suppose that Thelma and Louise are each served by independent tellers
immediately upon entering the bank. [3] (a) 60% of the time, the time it takes to make a withdrawal will be at least how many
minutes? Lef /\’ alena'l‘e ‘yle /ev7% of, 7Limc 7‘22 make a WI'7q7z/rawa/.
721cm X’V EX/acmemL/a/ (Q = V?) aha/so PKX>X) = aux/8) X20
We wfsA 7L0 O/EéI’mine ‘LL sac/7 7%a7L FCX>f) = 0.4:
6—178 = aé "f/s =/nO.é
'6' = “8570.63 777(6) hL +a/(es_ 47L /eas+ 087m1'nu7l‘es 1L0 make a WI'7%/ra wa/ 60 % maﬁa 7‘7!!! [3] (b) What is the probability that Thelma ﬁnishes service before Louise? 16+ l/ Jena 5 '6‘): kry‘ﬂi 07a 7L/me "/22 Furcﬁase ma7zua/ 744ml:
.7716”) Y’V EXFonen‘hﬁ/éﬂ: l/l? ), P(7l12.lma 'pinishes loaflore [DU/3‘8) = T“ — __._‘t_ = i— [3] (C) On average, how long does it take for the ﬁrst service to ﬁnish? 1.8+ T O/QH07LG. {be {II/77¢. f0 7%: #if'sflSElﬁ/I'ce camf/gfigrh
72k") 7—: "7"” YENEXFonaﬁL/a/(‘TgL + 7% = 97:4 = .4:— I
771113) = ,3/72 =' gag 5538Minu+é5 [3] (d) It is observed that after 13 minutes Louise is still being served by her teller. What
is the probability that Louise’s service time will be at most 19 minutes long? We Wish +0 cia‘f'ermine. =F(y\</3+G/Y>/3) =/0(Y\<é) é 797a menu»— 4555‘
= /_ﬂ 5 6/0] Fro/every 3 0.2835 2. For a branching process having X0 = 1, calculate the probability that the population
will eventually die out when the number of offspring (produced by any one individual) '
has probability distribution given by: (a) P0=1/8, P1=3/8, P2=1/4, P3 Firs‘l) We caiculn‘i’g/u =. = J=D (Sich 7/) 7/7; is IL/ve SMa//es+/005}’7l‘ive 50/147901: 5a7LLs'P/iv
. 3 ,
m=zmw
d :0
77: 73+ %=7/3+%;7/22+ ﬂf/f 277i+275£57c +/ =0
(742—0 (2m2+4m—/)=O
7/3=/ rive —/i 1/2: K $7etl'hea/ Via ZuaJra'l‘I'c grinqu 77m) Wasee‘i'l’la'i' 7):: — 1+ 52: r: 0,225. [4} (b) P0 = 3/5, P1 = 3/20, P2 = 1/12, P3 = 1/6 Fins7: We ea/cd/m‘e/M = =C/)(%a)+QX%z)+(3)[%)
4—; 4%0 Sl'nce/M< /) we Can conc/uc/e. 7990171“ 7F:/. ...
View
Full
Document
This note was uploaded on 07/12/2010 for the course STAT 333 taught by Professor Chisholm during the Fall '08 term at Waterloo.
 Fall '08
 Chisholm

Click to edit the document details