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Unformatted text preview: Economics 41 UCLA Fall 2008 NAME (Print) November 17, 2
Midterm Exa TA Name & section timéui  The normal table and some formulas are on the last page ofthis exam  Only pens, pencils. and erasers may be used — this is a closed book, closed note, exam.
 Students may use an ordinary calculator, but nothing that can access the internet. _ This exam consists of [5 True/False ? (30 points) and 10 short answer ? (30 points) and 4 problems (40 points).  Clearly write answers on this exam. No points are awarded For illegible answers.  Report decimal answers to 3 signiﬁcant digits.  Be prepared to show a photo ID during the exam (e.g., UCLA ID, driver’s license, or something similar).  You may leave when finished. Turn in both the exam and your scantron. Do not disrupt those still taking the exam. 1. Circle either T for True or F for False (2 points each, 30 total). 1) T ([email protected] = total gross movie revenue. X = number of movie theaters in which the movie is shown. The correlatiOn
between and Y will be larger il'the top 100 ﬁlms are considered, rather than if lOO randomly sclcctcd movies were
considered instead. 2) T [email protected]¢\ssume there is no causal relationship betneen X and Y; but that an increase in 7.. causes both X and Y to
decrease. The measured correlation between X and Y will be negative. 3 or F The correlation between X and Y is .5 for observations based on average values from 50 states. lithe
correlation were calculated from data on l0,000 individuals, the correlation would likely be smaller than .5 [email protected] F [fthe sample is a “simple random sample,” (SRS); each individual in the population has an equal chance to be
inc uded in a sample. @r F Sample proportion, p (“phat”), is a sample statistic and NOT a population parameter. Gar F The Central Limit Theorem states sampling distribution ofthe sample mean gets closer to a normal
distribution as the sample size increases for all samples (even iffrom nonnormal population). 7)@r F lZach parameter has one true value, but each statistic has a distribution of possible values.
891' F Use of the normal approximation to the binomial distribution would .\OT be appropriate ifp=.9 and n = 50. r F Given probability p of success. ifthe number of“trials,” n increases. the standard deviation ofthc sample
proportion \\ ill fall, but standard deviation of the number of successes will increase. IOQr F There are four ways to choose a committee 0f3 people from a group of4 coworkers. . writ? l/llfyl’ﬁ‘ﬂi
ll 1‘ F A portfolio can not have a higher return than the returnslofeacl) ofthe individual investments. r19 11me 12) T o®f two events are independent, then the probability ofA 3B = probability ofA times probability of B. ”@r F If two events are disjoint, then they have no outcomes in common. ”Qt F Benthrcl‘s Law implies that the probability ofthe ﬁrst digit of numbers in financial documents is more likely
to e l than 9. 15) T Mai} returns on two assets have correlation =  I; then any portfolio that includes both ofthese assets will have a
standard eviation of its return = 0. A: Ciﬂttéﬁd Pram mam/l I) Toss a fair coin (so heads and tails are equally likely) twice.
What is the sample space? (i.e., what are theMdifferent possible outcomes and how likely is each?) et a random variable X= the number of heads in these two tosses (order of the ft_os_es doesn’. t._ For“ Stilts 2 Wat/5 2) Toss a fair coi matter). X p6!)
a) What is the mean ofthis random variable X? 0 1] Molt 30H 2503* I v M 1,49%me
b) What is the variance of X? I I Z J' 41 144/)
DilWCi .Tgﬁrllzt.§(t~rlzf,t§(2u : .25”? 1' g‘: in P0”; 1 h" ,i t“ ‘an’i‘f’j’
c) What isthe standard deviation of X? S— : g 707 r 151;) ti p‘x—éﬂi‘ i
,I' J amid/7, / . ‘  _ . . . ‘ : 2’ . 2.
—m tax: ‘S‘Ellf‘Z/UHBUJ . 961% EA (Xi/u]
_;+o+.a:~.z £93 A 0/4
a $0 a t 2mm 20 : I§( 154) 7‘“ 2691/) L .3044)
2? 31+ 0295) 7".‘132 3'76 4) F01 X in the above problem:
a) What Is the standard deviation of ?_p__& b) ls this a statistic or a (citcle correct)
D 5) Asset X has a return 0 ' ith standard deviation oﬂ'W
You invest 50% ofa port 0 10 in asset X and 50% in asset ' a) “/1th IS the mean percentage return ofthis portfol {
Mr stew 9(2)  a t! W" nd asset Y a return @v ith standard deviation 4f 3%.
e sure to show how you set up this problem to solve) D . > : 12.29+2.2€'+8¢i e 22.51 $2 desiring}— M i0) lftrue correlation between X and Y = .8, what is the standard deviation oftliis portfolio? LL 7,2 g PERMiv :(§12(7J2+C§J2(3)2’ 4. 2 [335(7) ,§{3J 2_ 0r mt : miewc/xm
A 6) Consitltr two events, A and B. P(A) = .4 and P(B) = .3 ,2
a) If A and B are independent, what is the probability that both and B occur“? RQA8):[email protected]~HQJ:: Gng3):.1~ b) If A and B are independent, what is the probability that neither A nor B occur? l>(/l[):'6 )%Cj:.7 {kW/1 RC):(6)[7J 7. Hz
c) lfA and B are Eisioiéélwhat is the probability that both A and B orient? Panr 1 7) The following table is for a s ple ofSOO men in who are patients a a pal Icu Smoker NonSmoker Total:
Have Cancer: @ 60 3O 90
Do Not Have Cancer: 90 320 410
Total: ISO 350 500 Select an individual at random.
a) What are the unconditional probability they are a smoker? £0 1 g
930 ‘ b) What is the unconditional probability they have cancer? 3,95 :1 [g
. S‘ﬂ . A c) What is the probability they are a smoker, given they have cancer? $1: a ma} In [16
b) Show smoking and cancer are not independent by comparing you! MoEonditional probabilities with the& elevant unconditional b) Is the number 0 arts in a fixed number of draws with replacement a binomial random variable? c) Suppose you_do not place the ti 0,
5 at X = the number successes in ran om samp e , l tty of success is .l for any one o serva ton. What is the probability ofexactl 2 successe ' 9 Use the appropriate tormula on the last page to show #9“:
45/ I y I" l _ I 
you vok. Q_ 61J2(5U {  ﬁg CDDbgblb 5‘ 96 HP l 2* ' the probability you draw two hearts in a row? Ill. Clearly, concisely, and completely answer the following problems. (10 points each, 40 total).
SHOW YOUR WORK (e.g., the equation you solve, or the ratio you compute) 1) Consider the ontime arrival data for two airlines Northeast Air and Southeast Air for ﬂights from 11A: Northeast Southeast
Destination On—time Delayed Ontime Delaved
Detroit 800 200 75 25
Houston 95 5 900  00
Flights to Detroit and Houston  AGGREGATED
3) Aggregate this data and ﬁll in the table to the right: Ontime Delayed
Northeast
Southeast ‘ﬂ—u.
.. /" I 30
NM 5' l
b) What is the peleent of ﬂights on time for Northeast Air lFor Southeast Air? 996. e) lfyou ﬂy halfofthe time to Houston and l1aifthe time to Detroit, must always ﬂy on the same airline, and arriving on
time i .   *    1er things like price and safety are the some), which airline uould you choose? I) (ﬁll in the blank) This example above is an example of" 601m 0633 \Jtl‘sm n A
2) Two assets X; X; and have the same mean return — 10% = u, = u; and standard deviation _ 2% =crl= o; and the true
cmrelation between returns on X; and X3 = 0. a) You invest 50% ofa portfolio in asset X1 and 50% in asset X2; A ‘ v1 /‘ or ’Semm‘“
I) What is the mean return in “/11 ofthis portfolio? [0 90 w [3.9“ 91/11! [ Dipml’ ””0” e d I
r
'2. “—H ii) What is the variance ofthis portfolio? 0.3361 z .271le ,8‘[211+o = ﬁ(4443:@2/Mf””* 15— xi lug X;
iii) What is the stand  viation of this portfolio? otﬂt h) Suppose you im oktﬂ5%' 1n asset X]; 25% in asset X3; 25% in asset X3; and 25% in asset X4; true mean ot‘all
indi\ irluttl Ill\L>tlTlCl1l3 X 15 ux— — 10/0, true standard deviation of all ind vidual invest nts is 6x — —2%, and correlation eween 1em= 0 _L l j 2
bi)lWhat ils the variance ofthis portfolio? 0—??— ?" ((7)123 7L (:7)? 27Lf) 2 2/2;
: Ti; 4+ q i'LHL/B : ’Lg ;@ porezl ii) What is the standzud deviation ofthis portfolio? \IT [email protected] With/1i
2 ijhalﬂf' gamma it? VFWW‘A A B ’95— 3) Suppose 4% ofathletes take l‘IOI mone s A test is positiwe efor 99% ofthe athletes who do In fact take hormones, and
(Fttlsely) positive for 10% ot the athletes who do not in tact take hormones. Pé)‘ .. Ile p B [4‘]: I9 61 . .I I . . . I _ 3/4( ) ‘” I ) D
a) What Is the probIIbIlIty that a mode I . osen athlete does not take hormones?
C _‘ _
Ml 3' I‘M—We; b) Find the probability that a randomly chosen athlete takes hormones given that they test p05ititc.
PQleB H33: PGM P I : “(UL/i :ngqb
{Blﬂrlpﬂl ‘l PSl/tCJ/JQC) . .0396+,Wb c) Find tlte probabilitx that a randomly chosen athlete does not take hormo :_ '. est positive. 2mg) PﬁM‘l/t J
’ III/r”) PQCHP (4)1985 096+ “3675 ,l3.6: d) What is the unconditional probability that a randoml chosen athlete tests positive.
[3&3‘: PéI/IWMHLBI/IJPQI =1 4) t a gwen c ory o o the tar rives are e ectwe. Two hard drives are randomly chosen. Let X = number
defective in this sample of2. a Use the bino IIiaIl distribution to find the probability for each of the possible \ alues of X. onsider the factory above. Suppose a sample of [00 hard drives IS taken. : ' se the N: I . . I . I nation to the Binomial to ﬁnd the probability that 14 or fewer herd drives In the so Imple at L
defective se the continuit correction. ., _
( B'n a__ ) y _ ._ é ILLS 5‘30): “I_P(Z L LII/(r) c) Use the Nmnml approximation to the Binomial to ﬁnd the probability that X= 14 (must use continuitv correction) mm 2 (I III IIIIsw Iqeaz — Pé. 45%;”) U ...
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