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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 (“p-hat”), 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 non-normal 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 co-workers. . 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 PERM-iv :(§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 Non-Smoker 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 on-time arrival data for two airlines- Northeast Air and Southeast Air for ﬂights from 11A: Northeast Southeast
Destination On—time Delayed On-time 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: On-time 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>tlTlC-l1l3 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 ;@ pore-zl- ii) What is the standzu-d 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.
PQle-B 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 III-Isw Iqeaz -— Pé. 45%;”) U ...

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