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Unformatted text preview: Prebabﬂity anci Statistics fer Engineering {ESE 326) Exam 1 February 18, 2131(3 This exam coniains 1.1 muitipie~eheice prebiems worth two paints each, six {memfaise problems worth
one point each, seven shariaanswer prehiems worth (me pain: each, ans ens freemrespense prebkem werth ﬁve points, fer an exam tom} of 40 pemts. Part I. Muitigle—Cheice {two saints each) Clearly {iii in the ova} 011 your answer card wlﬁch certesponds to the cniy correct response. 1. Each time Acme Scepiies lands a new customer, as eighbcharacter alpha—numeric cede for that
customer is generated randomly by a computer. Each character in such a password can be chosen
from among the 26 letters A—Z and the '10 digits 0mg. Repetitien is snowed. What is the probabiiiiy
that a randonﬂy»generateé password of this tyce contains ski letters and no numbers? (A) .0095 '
(B) .0299
(C) .0223
(D) .0386
(s) .0515
(F) .0740
(G) .1365
(H) .3712
(I) .2523 2. What is the probabiiity of getting a “straight ﬂush” in a ﬁvecard hand deait frem a standard deck of
52 cards? (A straight ﬂush is ﬁve cards in a. row, ail ofthe same suit, such as 31!, 41!, 5*, 6V, ’E’V.
Em. An Ace can be 10W or high. In other werﬁs, both the straight A, 2, 3,4, 5 and the straight
10,.1, Q, K, A would be aﬁowed. (A) .0090092
(18) 3090139
((2) .eseezss
(D) messes
(E) .9004?98
(F) .csessss
(G) .sezssss
(H) 3039245
(I) cessseo
(5) .essssss La Bekah, Kemiaiﬁ, anti Mary go shopping far shoes. 2%.: Fortuitous Feotweag there are 250 styies 0f
l3dies‘ shakes. Eagh teen pians to buy (wither one pair or twe different pairs (day (it‘s OK if
muitipie teens choose the same gawk.) Haw mars}? outcames are possible? (A) (259)3{2530233 (B) (250)3{25313 233 (C) (3)(359}3(2596233
(D) (3)'{250}3(250P2)3
(E) (3)[250+ 25802] (F) (3) [250 + 259332]
(G) [259 + 250643
(H) [250+ ZSUPQF (I) (250?(425002):3
(I) (250)3H256PQ3 8% of Americans have diabetes( £294; have chronic kidney disease (CKD), and 9% have CKD but
not diabetes. What is the probabiiity that a randomiy—selected American with diabetes also has CKD‘? (A) gi;
(B) :3;
(C) i
(D) :3
(E) E
(F) g
(G) S—
(H) :2
(I) g.
(I) g ’5. 15% of Americans ever 38 years 0f age have earned an advanced wiiege degree (mything beycsnd a
bache§er’s degree}, Of Mexicans ever 30 with advanced degreeg, 22% earn ever $1812}. 09$ per
year. Of Americans over 39 without advamed degrees;, 6% earn ever $26K), 009 per year. If an
American ever 361 earns over $196,090 per year. What is the probabiiity that he er she has; an advanced (iegree? (A) .Oéég
(B) .948}
(C) .2???
(D) .3529
(E) .3929
(F) .6€)’?1
(G) .6471
(H) .7273
(I) .9519
(I) .9541 6. Consider the fei'lowing ﬁmctien, which is potentially a density function for a discrete ratadom
variabie X. ﬂan—f; xm2,3,é,...
What wouid the value at" the constant c have to be in arder to make f a density? (A) .1... @
mi“ own rmw wzw NH M (C)
(D)
(E)
(F)
(G) 3 (H) 4
(i) 12
{3) :6 7’. The number of “hits” to a certain website is a Poisson process with an average of '5 hits per hour.
W’hat is the probability that the website wiil receive exeeiiy 1.»; hits in a twwbour period? (A) 13521
(B) .0663
(C) .0835
(1)) .i?57
(E) .8243
(F) .9155
(G) .933?
(H) .9479 Newt Isaaes is somewhat prepared for his physics ﬁnal exam, which Wiil consist of sixty questions.
The probabiiity that be win answer any given question correctly is .175. What is the probability that
Nev/i Wili. answer between 45 and 50 (including 45 and 50) questions correctiy? (A) .4054
(B) .4294
(C) .4524
(o) .4764
(E) .5236
(F) 54%
(o) ems
(H) .5946 There are 1200 booby birds on Espaﬁola, (one of the Galapogos Islands), of which 750 are biue~
footed boobies and 4158 are masked boobies. (Yes, these are reai species!) If a naturalist captures
16 booby birds at random points around the island for study purposes, what is the probability that at
least eight will be ﬂue—footed? (A) .01
(B) .05
(o) .15
(D) .21
(3) .79
(F) .85
(o) .94
(H) .99 If} A mlieybaﬁ mach holds a serviag competition for her team members Each giri makes repeated
attempts t0 serve the baﬁ over "the net anci in bounds (a geed serve). When she has reached a total
of ﬁve pom serves, her turn is over, and the totai number of attempts (gﬁad and p901") is counted as
her score. The git} with the highest scare wing. Jcrdan can manage 21 goes! serve 72% of the time‘ What is the probability that her scare wiﬁ be $3? (A) .0836
('13) .0094
(C) .9615
(D) .9984
(E) .1806
(F) .8409
(G) .9016
(H) .9385
(I) .9906
(J) .9964 11. Let X be a hypergeometric tandem variabie with N 2 24, ’r = 20, and n m 8. What are the
possible values for 3:? ' (A) 0,1,,..,4
(B) 0,1,‘..,8
(C) 0,1,...,20
(D) 1,2,...,4
(E) 1,2,.,.,8
(F) Lanna
(G) 4,5,...,s
(140415“..30
(I) 8,9,...,2ﬁ (J) 8,93,“,24 P311211. True~Faise (me paint each) Maxi: ‘A” an "yam answer card if the statement is true; mark “’B' if it is faige. E? “i 13. 14. 15A 16. E7. If A anci B are events such that PEAEBE m 0, then A and B are mutuaﬁy exciusivet Suppose A and B are events such that PEA} m .75, PiBE = .6, and PM U B] 3 .9» Then A and
B are independent. If X is the ameunt of time that goes by until a light bulb burns out, then X is a discrete randum
variabie, Suppose X is a discrete ranciom variable With E[Xj 2 12 and (TX m 3. Then, according to Chebyshev’s Thearem, P33 < X <: 21] m "g. 2
Let X be a discrete random variable. Then EEX2 + X ] m (EIXD “1”” E 1X] The St. Leuis Rams play 16 games éuring the regular N&tional Foetbaii League season. Let X be
the number of games wen by the Rams during the season. (There are no ties, 011E}: wins and 105535,)
Then X is a binomial random variable" Part III. Shaft Answer {me peim each)
The answer to each of these is right or weng: n0 work is requﬁed. and no partiai credit MB be given. 18. Ellie is one of eight swimmers competing in the 260 yard butterfly event. Why would it mt bra
appmpriate to say that EEIie‘s prokahiiity 0f winging the event is Q? (The reasan can be stateci simply and brieﬂy. if you don’t knew, éoa’t make wmetﬁng £113. Yam answer Shanid be precise
and should use a tecimical term.) 19. Suppose that A and B are indepentient events such that PM; m .55 and PLBE m 32. Find
PEAiBE. For pmbiems 20 and 21, suppose X is a discrete random variable with ELY] 2 E2 and cu: m 3. 20. Find EBX ~§~ 8]. 21. Find VarGX ~§~ 8). For probiems 22 and 23. supgzsese X is a discrete tandem vaﬁabie with the foiiowing ﬁensiiy tabie. :c g 1 4 8 9
ﬂ}??? ,3 .2 .4 .1 2:2. Fﬁnd EEK; 23. Fill in the density tame far the random variabie X2. 3?
ﬁx) E
E
W; 25$. What is the varianse {if a negative hinomiai random variabie with 5*" 2: 10 and p =2 ,4? Write yeur
answer in decimai form. Par: 1V. Free Resgome (5 paints) Foiiow directions careﬁﬂly, and Show ail the steps needed :9 arrive at your selution,
25. "The foiiowing function is a memem generating functien for a random variable X.
mg (t) : .00932(2 §~ 3&3}5 (a) Use. the moment generating ﬁmctien to ﬁnd E [X] (1)) Use the moment generating function to ﬁnd Var(X) ...
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 Spring '09

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