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Unformatted text preview: ﬁebability arid Statistics for Engineering {ESE 326‘} Exam 1 Febmy 1?, 291‘: Thie exam centains nine muitiple—eheiee preblemg weft}: {we paints each, iha‘ee truefame problems
weﬁh ene gem: each, 18 shoﬁwanewer prebiems werth One pain? each, and {we freerespen3e prohEems
worth nine points aitogether, for an exam tetai 0f 40 points. Part I. MuitigieCheiee (two points each) Cieariy fiii in the med on your answer card which corresponds to the 0:11}! corms: response. E. Each time Acme Supplies Iancis a new custemer, an eightmeharaeter alphavnumeric code for that
customer is generated randomiy by a computer‘ Each character in such a passworé can be chosen
from among the 26 Eetters AwZ and the £0 digits GL4; What is the probabiiity that a randemiy—
generated pagswerd of this type contains no repeated ietters er numbers? (A) .0000}: (E) 390025 Qgﬁej <3“: I (a) .2523 W" ”“3“” 1" an? «£53 25*”
{D} .3013 3 519 e 3&5 (F) .56?5 (G) we; (H) m7? {1) .999975 (1) .999989 so In how many ways can six peeple be chosen from a pee} ef seven femaies and nine maies, where at
ieast one female and one male must be inciuded? {e354 NM 5:: f‘eé ﬂ
(3391 {jeﬁwié/J“ géjgi: "93%?
(C) 189 {:3} 882 (E: 19?: {F} 1268 »WMwa—M [M
““x 5 {H} 8008 {i} 63? 85:3
{3‘} 1; 5135512 3. What is the prokabiiiiy that a sevenucard hand dram {mm a siandard deck 43f 52 cards centains (me
three‘wofwaukind 311$ Wm (éifferentj pairg? {Am examp'ie {:sf 3 hand like this weuki be
5¢,§Q,Sv,Qv,Q¢,2é32v.) {1763: you peker aficianados, I mnéefsiandthat {he secsx75: paia‘ is
irrelavzmt singe {mly ﬁve 9)? ihe: cards; cam be: uﬁéizaﬁ, but Earner me 311% campuie the pmbabiiﬁiy amway.) (A) .0083 1/ f3 jib; Effgay ‘1? g]; £912 < ﬁfigfigagﬁlf »
KB} 709?”: WW MWWWW : f ﬂﬁﬁ?
@ f§3> (D) .8012 g M; (E) .0018. (F) .0024 (G) .00?4 (H) .0210 (I) .0222 (I) .0443 4 28% of American heusehclds own a dog but not a cat, 15% own a cat but not a dog, and 51% awn
either a cat er a dog er bath. What percent ofAmerican househokds mm both a dog and a cat? ex) 7?3%
m a {£3 12$§ $3) :3?6 (E) 16%3 (E3 20%% «3} 21%3 @&) 34%e g Q) éiﬁﬁ {3} agag LI: Suppose A and B are events such {hat PE 2: 4 Pig/1H8} 2: .75., anéi Pfﬁééj m .6. Find. PiB! [A .096 "E f” y r,“ f r} ﬁ A ”E _/ {”32 M? “5‘ 1' r( . 1‘ m. 5 _
H fig??? :5 :1 f} 5:753»; ,3 : 953%; w {Veggiig} w. £23;
{8} m4 _ {C} .18 :32 gag$52] :in’f’zgfﬁgéﬁéﬁj (D) .24
(B) .3
WWW A g ”E w w w .
5(5) .32; g“; LEE“ * WM ‘3: “£2“
MWJ at M? 5, g (G) .45 (H) .5333 (I) .6??? (I) .8 b»: Consider the population Of American maies ages 18 to 65. 70% if those who are 18 to 39 years old
(“younger guys”) are empioyeck, 92% of those whe are 31 to 50 years old (“middle—aged guys”) are
empioyeé, am? 86% of those who are SE :0 65 years old (“oider guys”) are empioyed. Withiﬁ this
whoie popuiation, 25% are younger guys, 60% are midéﬁaaged guys, and 15% are aider guys. if
an American maie 18 to 65 years old is employed, what is the probability that he is an 016$; guy? wmh. “M,D,W
: Q} T1507; 53/] : gig/«:m—yg/bﬁ. 43% M {/5 g" a '4 5
(B) 1578 {#2:} 9 M ”{Ejgwfgﬁ Hggﬁivj K‘gM aﬁﬁiﬁw “Mgr/y:
(C) $655 g i ”W " <3;
(D3 .31?
{E} .1789
(F) .1950 y. w? W M
(G) 2044 Pi €53 “ 25"
a s» Mg m :
{H} .2632 5? E, 2;; i » 2 M1
{1) ‘355: :3 35:} g, T £5:
{1) .6449 * “ ~45
5  ”E {,2 322$ 1235’: Raﬁ
P g {in} i g 1! “A: WWW ‘3:me :‘M “2“": g“ x
5327535233”; ; 5%3;&&6> «4 5’ a: £5” E;
if: 53/3”? Grandpa Den heiiis an egg hunt fer his granﬁehiiéren every Easter. Re puts a quarter in eaeh of 40
eggs and gets a deﬁar hilt in each 0f eight egge. if Kim ﬁnds nine eggs this year. What is the
pmbabﬁity that she gets exactiy twe 9f the eggs with (tenet bills? . .s‘w * f M W 81"“ M ’1
{A} ’00?1 iii.i%§g£f%m§é’%% .53 .. gig”? we .. § we. 1 %
ix".— , {B} .0988 f 3 . g . . es. .
{C} .911: §>§XfZE : {:Zémij .. “$3
(D) .054: .‘ggxz .. =
(E) .1359 { (F‘) .2472
(Gt .391 5"” M
(I) .3421? (I) .3662 Cowboy Bob ﬂips a coin every {fay to determine whether or not he Wiil take a bath that day. If he
gets heaés. he takes a bath; if he gets taiis, he (toes not. The problem is that he uses a weighted
coin (given to him by his gmnddaddy, Gambier Gus} which comes up heads oniy 40% of the time.
if Cowboy Bab censiders Sunday to be the ﬁrst day of the week, What is the probability that his
ﬁrst bath 0f the week will be on Tuesday er Wednesday? (A) .6864 Q. #@%g > & g 5
(B) .1344 55% f 2 . . 2. .
f). 1:432. P51? :23 .x. Xe] : 5.5.} {L9} é» 515.3 5%}
(D) .2304; (E) .3841} 7: . 2.353%;
{F} .6168
(G) .?696
{H} .8569
(1‘; .8656
a) .9136 ‘9‘. Than: are 2% studentg emailed in an imméucmry” anthrapgiggy mama Gf theme, 203 are: acimail‘y
in tha (£333? and five are 011 the waiﬂigi. Suppase there is a 2% shame that 2111}? given student
ammg {hit 209 WEE withéraw earl}; emugi‘: in the Semestar It; aliew SﬁﬁlEOﬁE fmm the waitiist Se be
admitéeii inw the Class‘ {Yen may asgmne thai méihdmwais an? indepenﬁent 0? {me anoihaz‘. and
yen may aiso assume that .119 one from the waiﬁist mithcimwg.) What is the probabiiity that 33 the
students; on the waﬁﬁst wiif get Emit) the class? {m,m% éggm®@g ﬁzﬁﬁﬁﬁ §>$5£E (B) gym M (C) 2815 PEXEESE EEW'PEXEEEE
L“? W] W . __
(E) .4886 “‘ aéZéﬁ‘aw wﬂng
(F) ‘5994 ((3 ,6288 (ED .?185 a) .?867 (I) .8914 Part II. True»False (one point each)
Mark “A” on your answer car& if the statement is true; mark “B” if it is faise‘ 16. For any events A and B PEAEB’EM M 1 w PEAEBE.  m 3z3m {iv/WM ‘Wéﬁjg £5,3ng if (Lazy? {##3ng if; @1me
E R if .7 , ‘ ,
W “ .533, M“; j E3 “Em/x ’Ev’iaﬁ éﬁyuxm {'13 a, 5/: “Egg gsgﬁéﬂixzamﬂi’ig
,' if ikmi iii 1%.. Let F be the camuiative distribution function for a discrete raniiom variabie A. If x} g x3, than gram £44,, ﬂu, a.g‘&..§«§g7é ff 8 , sé ’? f E ”’i 2
ﬂ 3%. “Law. 5:“ ﬁaawwwggaga; fE/wig‘zaéwgé}, E mi M WM at ﬂé’ﬁﬁéﬁyhgmgff? fiéééﬂ,£;2~i_.§’}€ ‘
i“ 12. Let X 3:36 a discrete ranéom variabie. Thar: fer any reai amber}: c, an); m sax, faww vagjsé’ w gﬁgﬂ; Pan? HI. Sheri answer {one pram: each}. The answar ta each 0? these is right car wrang: m3 wmri: is required, and mi) partiai credi? WEE} be given‘
Géve (311%); one 531332133" is eaeh, (If you gisse mare than em answer, me pasta? one wiil Gaunt} Far any
pmbiem requiring a numeric3% answer, give a numaricai answer, net 31:31: a femuia 03' an unﬁnished
camputaﬁm. i3. What": singie aﬁjecﬁive dascﬂbes a phenamenon fer which may individual remit is unpredictahle, bui
a pattern emerges in the tang run? Eﬁawmygwg 1.4. and 15. Let A and B be events such that PEAE m .3 and FEB] 2: .5. Exactly two of the foilowing
Statements about A mid B are true. Which ones are they? (I) If A and B are mutualiy exciusive, then P EA U B} a: 8. 3/!
(II) If A and B are mutuaily exclusive, then PEA ﬂ BE 2 .8.
(HI) If A and B are mutually exciusive, than PM U BE m .13.
(IV) If A mad B are mutuaﬂy exciusive, ﬁler} PEA 5‘? BE 3 .15.
(V) if A and B are independent, than PEA U B; r: .8. (VI) If A and B are independent, then PEA {”3 BE 2 .8. (Vii) IfA and B are independent, than PEA U BE m .15. _
(VIII) if A and B are independent, than PEA 5“: E 2 .15. w" Fer probiems 16 and 1?, suppose X is a discrete randem variable with ,u: a 50 and 0’ a: . i6. Fina Van(3X + 4), 3 e. , £3. W fﬁl‘; 1 M finkg ,y’k W ”W, EM {3% ME} ,. ﬁixwX w {Maﬁa} w ﬁéa 1?. Fiﬁin the biank: ff“
2% W Awarding to Chebyshezz‘s1nequaiiiy,PE42 < 55? < 58E _ W E f‘w W W
,2: é; 133 19K 20. 21. Below is the density fer a binomial tandem variabie with n 3 iii} and p 2' .3, except that the values
to which the female applies are missing. Fiﬁ them in. f<$}e(%8)(.3)“‘(73n“$ s: e g) 2} 9 ea} 3 Given a Bernoulli trial with constant probabiiity of success 39 2:: (16, what is the average number of
triais needed to obtain {we successes? RE ".5“: g: * £3“ a“: «v ('2 '3  i;
?”e£»;.§eimfﬁ, awesmeeeﬁ “’3‘; ”I '2 3””! g Egg
s: M {W W #3”;
g: g: X e W '3: g3. *5
g g e ’ " Suppose Ehere are 60 marbles in a bag, of which 25 are biue. What is the average number of biue
marbies in a sample of size 18 taken from the bag? £133; .ma;_,,uwmfz:m 33,} répiﬁ Me: if ”3’5; 3’ Egg
if j K? 333:3 5/; 0,. w W: W M iigj” ngsege :23 Suppose X is a hypergeometrie random variable with 3‘5 x 2006, r x 53, and n. :2 2%. Since 3? is
Earge relative :o m the hinomial distribution may be used to approximate the hypergeometric
distribution. What value of p sheuid be used? 52:} g
”k j: W w” ., a“, f .4W
1W, Ezﬁée; ‘9 5:)“ 35:; 93:13}, E‘me fiemange (paint vaiues as shemm} FGEIQW directians carefully, and Shaw ali the Siﬁ§33 needeé {a arrive 31: yam saiuiien. If you Wish {0
mum any gamiraers, round a} fair decimai giacea. {6) 23. Cansicier “aha discrete martian: vaﬁabﬁe X Whese density is given by the faiiawing tabi’e. g i 1 2 4 8 :ﬁ
fix); .g ‘ .ag mg .OQGQ 30009 {3) Find E {X}. jg»; {$33555 2%K/Zgﬂa}%§g§§§& g;%/,§}Z/sg:é W!¥§€_£d&ﬂu ”4%,me 5,; :3 y 5? we: :: 52;;5; {:3 :; g g
I a; ﬁ i“?
if») > 1' ma. . m “:m‘dw“ h, I i .auo ”‘99 {13) Find waxy ngw'yyagayiévéﬁx gm 5;?» 1" g Q; x21 “—1 (:1; :E 5/; a} a»? «:2;
”a 3?:Mwwiwm ““ng M W
gm; 322 y i; AM
£53"
‘3“ 2 W
Van3 :g’wass‘zﬁ’E *" 2J¥3?3 "P 2%; (c) Find ax, ’3‘; ﬁ’xég‘wgw‘ :: ”95%; {3} 24. Find ﬂue derivative 0f mﬁﬂm A“ 'Eie’iV with respect t0 i. Yen do mt need to simpiify’ your answer: war :10 yam need t0 ping m anﬁhmg far i. ...
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 Spring '09

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