Multiple Choice. Choose the one that best completes the statement or answers the question.

Transcription

1 ECON 56 Homework Multple Choce Choose the one that best completes the statement or answers the queston ) The probablty of an event A or B (Pr(A or B)) to occur equals a Pr(A) Pr(B) b Pr(A) + Pr(B) f A and B are mutually exclusve Pr( A) c Pr( B ) d Pr(A) + Pr(B) even f A and B are not mutually exclusve ) The expected value of a dscrete random varable a s the outcome that s most lkely to occur b can be found by determnng the 50% value n the cdf c equals the populaton medan d s computed as a weghted average of the possble outcome of that random varable, where the weghts are the probabltes of that outcome 3) Let Y be a random varable Then var(y) equals a E[( Y µ Y ) ] b E[ ( Y µ Y ) ] c E[( Y µ Y ) ] d E[( Y µ Y )] 4) The condtonal dstrbuton of Y gven X = x, Pr( Y = y X = x), s a b c d Pr( Y = y) Pr( X = x) l Pr( X = x, Y = y) = Pr( X= xy, = y) Pr( Y = y) Pr( X= xy, = y) Pr( X = x)

2 5) The condtonal expectaton of Y gven X, EY ( X= x), s calculated as follows: a k = y Pr( X = x Y = y) b EEY [ ( X )] c d k = l = y Pr( Y = y X = x) E( Y X = x ) Pr( X = x ) 6) Two random varables X and Y are ndependently dstrbuted f all of the followng condtons hold, wth the excepton of a Pr( Y = y X = x) = Pr( Y = y) b knowng the value of one of the varables provdes no nformaton about the other c f the condtonal dstrbuton of Y gven X equals the margnal dstrbuton of Y d EY ( ) = EEY [ ( X)] 7) The correlaton between X and Y a cannot be negatve snce varances are always postve b s the covarance squared c can be calculated by dvdng the covarance between X and Y by the product of the two standard devatons cov( XY, ) d s gven by corr( X, Y ) = var( X) var( Y) 8) var( ax + by ) = a b a σ + b σ X Y σx + σ XY + σy a ab b σ + µ µ c XY X Y d aσx + bσy

3 9) Assume that Y s normally dstrbuted N ( µσ, ) Movng from the mean ( µ ) 96 standard devatons to the left and 96 standard devatons to the rght, then the area under the normal pdf s a 067 b 005 c 095 d 033 0) Assume that Y s normally dstrbuted N ( µσ, ) To fnd Pr( c Y c), where c < c c µ and d =, you need to calculate Pr( d Z d) = σ a Φ d Φ d ( ) ( ) b Φ(96) Φ( 96) c Φ( d) ( Φ( d)) ( Φ( d ) Φ( d )) d ) The Student t dstrbuton s a the dstrbuton of the sum of m squared ndependent standard normal random varables b the dstrbuton of a random varable wth a ch-squared dstrbuton wth m degrees of freedom, dvded by m c always well approxmated by the standard normal dstrbuton d the dstrbuton of the rato of a standard normal random varable, dvded by the square root of an ndependently dstrbuted ch-squared random varable wth m degrees of freedom dvded by m ) When there are degrees of freedom, the t dstrbuton a can no longer be calculated b equals the standard normal dstrbuton c has a bell shape smlar to that of the normal dstrbuton, but wth fatter tals d equals the χ dstrbuton 3

4 3) To nfer the poltcal tendences of the students at your college/unversty, you sample 50 of them Only one of the followng s a smple random sample: You a make sure that the proporton of mnortes are the same n your sample as n the entre student body b call every ffteth person n the student drectory at 9 am If the person does not answer the phone, you pck the next name lsted, and so on c go to the man dnng hall on campus and ntervew students randomly there d have your statstcal package generate 50 random numbers n the range from to the total number of students n your academc nsttuton, and then choose the correspondng names n the student telephone drectory 4) In econometrcs, we typcally do not rely on exact or fnte sample dstrbutons because a we have approxmately an nfnte number of observatons (thnk of re-samplng) b varables typcally are normally dstrbuted c the covarance of Y, Yjare typcally not zero d asymptotc dstrbutons can be counted on to provde good approxmatons to the exact samplng dstrbuton (gven the number of observatons avalable n most cases) Essays and Longer Questons 5) Followng Alfred Nobel s wll, there are fve Nobel Przes awarded each year These are for outstandng achevements n Chemstry, Physcs, Physology or Medcne, Lterature, and Peace In 968, the Bank of Sweden added a prze n Economc Scences n memory of Alfred Nobel You thnk of the data as descrbng a populaton, rather than a sample from whch you want to nfer behavor of a larger populaton The accompanyng table lsts the jont probablty dstrbuton between recpents n economcs and the other fve przes, and the ctzenshp of the recpents, based on the perod Jont Dstrbuton of Nobel Prze Wnners n Economcs and Non-Economcs Dscplnes, and Ctzenshp, US Ctzen Non-US Ctzen Total ( Y = 0 ) ( Y = ) Economcs Nobel Prze ( X = 0 ) Physcs, Chemstry, Medcne, Lterature, and Peace Nobel Prze ( X = ) Total (a) Compute EY ( ) and nterpret the resultng number 4

5 (b) Calculate and nterpret EY ( X= ) and EY ( X= 0) (c) A randomly selected Nobel Prze wnner reports that he s a non-us ctzen What s the probablty that ths genus has won the Economcs Nobel Prze? A Nobel Prze n the other fve dscplnes? 6) The heght of male students at your college/unversty s normally dstrbuted wth a mean of 70 nches and a standard devaton of 35 nches If you had a lst of telephone numbers for male students for the purpose of conductng a survey, what would be the probablty of randomly callng one of these students whose heght s (a) taller than 6'0"? (b) between 5'3" and 6'5"? (c) shorter than 5'7", the mean heght of female students? (d) shorter than 5'0"? (e) taller than Shaq O Neal, the center of the Mam Heat, who s 7'" tall? Compare ths to the probablty of a woman beng pregnant for 0 months (300 days), where days of pregnancy s normally dstrbuted wth a mean of 66 days and a standard devaton of 6 days 5