mid2A - Economics 41'CL Fall 2008 NAME(Print k‘flk UWWW...

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Unformatted text preview: Economics 41 ['CL.-\ Fall 2008 NAME (Print) k‘flk UWWW fl 1. 09%“ \ November 17. 20 3 Vi id ”UL Midterm Exa TA Name & section ti : ; H/r/lps — The normal table and some formulas are on the last page of this exam H - Only pens, pencils, and erasers may be used ~ this is a closed book, closed note, exam. 4 i - Students may use an ordinary calculator, but nothing that can access the internet. - This exam consists of 15 TruetFalse ? (30 points) and 10 short ansucr ? (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 (cg, UCLA lD, driver’s license, or something similar). - You may leave When finished. Turn in both the exam and your scantrou. Do not disrupt those still taking, the exam. 1. Circle either T for True or F for False (2 points each, 30 total). 1)@r F Y = total gross movie revenue. X = number of movie theaters in which the movie is shown. The correlation between X and Y will be smaller ifthe top 100 films are considered, rather than if 100 randomly selected movies were considered instead. 2) r F Assume there is no causal relationship between X and Y; but that an increase in Z causes both X and Y to decrease. The measured correlation between X and Y will be positive. 3) T ofgl'he correlation between Xand Y is .5 for observations based on average values from 50 States. Ifthe correlation were calculated from data on 101000 individuals, the correlation would likely be greater than .5 4®r F. Ifthe sample is a “simple random sample," (SR8); each individual in the population has an equal chance to be inc uded in a sample. 5g lzr F Sample proportion, 13 (“p-hat”) is a sample statistic and NOT a population parameter. 6) T [email protected] A well-diversified portfolio may have a higher return than all of the returns ofthe individual investments. 7) T o®ftwo events are disjoint: then the probability ofA or B = probability ofA times probability ot‘B. 8) T o®ftwo events are independent, then they have no outcomes in common. 9) 1‘[email protected]’s Law implies that the probability ofthe first digit of numbers in financial documents is equally likely to be any integer from 1 to 9. I0) T o®f returns on two assets have correlation = —1, then any portfolio that includes both of these assets will have a standard eviation of its return = 0. llQr F The Central Limit Theorem states sampling distribution of the sample mean gets closer to a normal dis l‘l ution as the sample size increases for all samples (even if from non—normal population). [email protected]'F l'ach parameter has one true value, but each statistic has a distribution of possible values. 1169” F Lise ofthe normal approximation to the binomial distribution would NOT be appropriate ifp=.9 and n = 50. .——_.— 14 F Given probability p of success, ifthe number of “trials," n increases, the standard deviation ofthe sample pit .ortion will fall, but standard deviation of the number of successes will increase. 15) T orB’here are six ways to choose a committee of3 peeple from a group of4 co-workers. 4. ‘3"L/ 11. Briefly. clearly‘ and correctly anSWer the following ten questions (3 points each, 30 totnl). 1) Toss a fair Coin (so heads and tails are equally likely) twice. PHI/labile“; What is the sample space? H A . 29 (ie, what are the four different 0 possible outcomes and how likely is each?) §_. ”—2 L 25 NJ \ z 5‘ T 7‘ . 2 § 2) Toss a fair coin twice. Let a random variable X = the number of heads in t1 ese twol sses order ofthe tosses doesn‘t matter). Pg?) 19’ , 5 :24“ a) What is the mean ofthis random variable X? i X 0 l 2 5 ~_ 2 5‘Q-bJ-Z 7’- 7fl ‘ i) 2': b) What isthe variance of X? ' 'Zé'tfl: U i- ' I ._ __I_— . .: earth/,1? '5 e) What is the standard deviation of X? I 7 D7 ”1‘5? 1 ‘ 7d '7 i6 7/? 3) A random variable X can take on three different values with the followingfrobabilities: o 1 -(gjio/aji i2): —.s40+.z=~.3 Probability 05 0.3 0.2 2 2 L a)\\'hatisthemeanofX?fll '§E’_623 4 [email protected]"—t35 + ’26....13 & = ($573Mafifrzfiafi:,‘2tis+.o2w.335’ b) What is the variance of X? t ‘6 I 4) For X in the above problem: a) What is the standard deviation of X b) Is this a statistic or a .1 ircle correct) 2. 5) Asset X has a return DMD/o with standard deviation Mud asset Y a return of2% with standard deviation M . “'3 lation be .. r-- I! I true correlation between ' 62‘- 8'5 + Zflitfirfisfl) O} :' m: 2 3.8 073’966 P : 95 +6 3 Mt? -pugml‘f ' 7... 6) Consider two events A and B P(A) = .3 and P(B)— — 3 a) If A and B are independent. what 15 the probability that both and B occur? mg): @1105): (31(3):. 11) [f A and B are independce t, what isth e robabilitv that neither A nor B occur? I I a) _ - 1361/19- ~ P5111? -[71[7J~-451 c) if A and B are disjoint, what i the prjbability that both A and B occur? P {11% :O 7) The following table is for a sample of 500 men in who are patients at a partioular HMO, Smoker Non- Smoker Total: Have Cancer: .50 41L__F.__—__9JJE Do Not Have Cancer: 100 3 l0 410 Total: _l_§0_ 350 500 Select an individual at random. 3) Wha®e unconditional probability they are a smoker? b) Show smoking and cancer are not independent by Wflonnditionalgobablh ' ‘ ' 6 two relevant unconditional probabilities you calculated above. Pg 1 C3- > W3): 9) a) A deck of52 cards has 4 aces. Ifyou randomly draw a card irom a deck then replace ' draw another card what 15 the probabilit) you draw two aces in a 10w? (1 J (I B ‘5 2, I Let X = the number successes in random samples 016 and the probability of success is .2 for any one observation. What IS the proba ' ' . - a show your work. of exact] 2 succes 1e of6'? the appropriate formula on the last lll. 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 LA: Northeast Southeast Destination Ola-lime Delaved -time Beloved Detroit Stltl 200 T5 25 Houston 05 5 000 100 Flights to Detroit and Houston - AGGREGATED 3) Aggregate this data and fill in the table to the right: On-time Delayed Northeast Southeast b) What is the percent offlights on- time for Northeast *0 51.9 r Southeast Air fig: 896 n til) What is the proportion of Hi 3 .- - me for Northeast Ait and Southeast gab __ c) Detroit: Nm-theast Ai HMO _ 8 For Southeast Air? (1) Houston: Northeast Ai e) lfyou fly halfofthe time to Houston and halfthe time to Detroit, must always fly on the saute airline, and arriving on- - - a ter things like price and safety are the same), which airline would you choose? tune is -- 5‘.” : W t take hormone nd 41- at: M at ' positive for 99% of the athlete. t in fact take hormones. PQH 13 c) Find the probability that a randomlv chosen athlete does not take honnones given that they test positive. P6 H3) FEW it” We) . Mt P MCHFWJ * WP) Swifts) HEMP") _Dlll3l-,039l> d) What. is the unconditional probability that a randomly chosen athlete tests positive. P635: Polo I enact 3) Two assets X1 X3 and hax- e the same mean retuIn = 10%— — [.L] = pg and standard dm | trion = 2% =01: o; and the true correlation between returns on X1 and X2 = 0. a) You invest 50% ofa portfolio in asset X1 and 50% in asset X3; i) What is the mean return in % ofthis portfolio? ‘ 5&0.) l- . géé _l, ;@ [gang/7 7L ": [/411fo ii) What is the variance of this portfolio?Z _ Iii: -. .5 (1331501: aflflewtazé’) 0757;; LS’CL iii) What is the standard deviation of this portfolio - b) Suppose vou investXZS‘l/o In asset X1; 25% In asset X2; 25% In asset X3; and 25% In asset X1, true mean ofall individual investments X Is 11);: 10%, true standard deviatiOn of all individual investments is ox— — 2% and correlation between them 2 0. 2 i) What Is the variance ofthis portfolio?U-P: C1532 22’ }é§'}2 7 2W Z #(2531 1a 2—120 ii) What is the standard deviation of this port - '- 4) At a given factory 10% ofthe hard drives are defective. Two hard drives are randomly chosen. Let X = number defective in this sample of2. 3) Use the binomia distributio to Within] the probability for each of the possible values of X. ._a,,-. 1., b) Consider the factory above. Suppose a sample of 100 hard drives Is taken. Use the Normal appr .. ation to the Binomial to find the proba il' rhard drives in the sample are defective, P(X3mm1® . correction '23 fl) Xxx/arm _. __=.4_m..u. c) Use the N01mal approx1matlon to the Binomialtofi _ the probability thatX 14 (must use cg tinui qeofi'ection) f3 ...
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