Prof. Bing Ma Department of Economics UMBC Econ 421 Introduction to Econometrics Problem Set 01 Question 16 STATA Practice: Question 16 STATA Practice: 1. Thv QTATA dim-i SM (lam 2UUIJETH mutains dam n13 hourly \""r'li'h. Mars 0f nt'hnnling 59x. yt'nt's uf Work vxpr'rivlu'v. l'H hi/.011 briltnh: .'xfl'it-am -Xmm'iran Shanta-u :mc'l Hispanir status of ulmur. 7M} warm-rs in 11w LUH Angvlua lllt'fI'upulimu arm. '1'lu- Hulllllt' is mkr'n frum rhu 1mm ('r'ums of Popularinu and m .1 large c'xrvm ir- still 1'v}.>rc-H'11r;lfi\\'s~ Hf rhv Lm Ahlmvlt-s lubur ft '1'! '1 2. Nm' ' It It'lmr'. F's-'0 rhv smrmmrize c-mnumnd in Sm'ra ha dvsvril'w rhv hum-1y wage variuhlr'. How many alm'rmrit 1115 .m' in rlu' samplv'.' When is rhv 111mm mum in the munplr'l' What is rhv maximum mm\" in fhv mmplt-Z' 'l'lw 111inhmuu'.' 113v Hamlnrd (l1 'viuti: )11'.' {Eur rim [st mnumuztl in Stun: In list thv \"125:0 nf ('vc'ry \"urkr'r in the #:1111910. \\Vlmt is TlH' l'lulll'l' may of tho rm Wurkm' in T110 mmplv'.' What i:- rho hourly W21 :10 uf The! last Wurkor in rhc' 5211111310? (yum (in 1:01" ne'vd Tn print this lthlI' is run lung) (hush-um u hismnl'umnfrllv wun'v m'iuhlv using the "In )1: rrsu'nnetml. lb Flk1'{li>rl'ililltirlll h i') hiivwml I'm tht- lvfr 01' l'igixr? Wages and mrningas urn nfrvu studiml by hit? talking logarithm (N! )W: in this. Human all logs 2111- natural logs}. Tram-form the wage variahlv by taking its lugatmn using the: t-nn'ummd generate and dip func-tiun In. Hm: rt'pm't thv 111mm value of fhv lugt'wag'r') \\m'iAhlv. IIM' fhn fable ('l unmnml ft) :11 H 'l'ihl' rlw fl'('(11'l'1t'il'E-' of yt'al'h c If H'hl >1 ing (\\'ill'lllllf' wlm'utiu) -) HOW many wurlwrs have (-'XCllY a highmchuul (lf-'gi'i' (12 \"nu-:4). I'Iuw many haw (Ixar-tly a H.3llvgp (logrm' Iltj Wars)? IIrm' limnv haw ur Ivar-t a mllvgv (lt'grvt'? Arufln'rv m )rk' '1' wlm 11mm \"'r'nr tn svhuul'.' {king only r110 i1'1fnr11mtiun LIiHI'lemwl in rlw mva (and a c'uk'ulamr) valvular? fhv ave-Tags: 3'0;er of sctlmnling in rho r-an'mlv, l'Hv rlzv Sham e-unnmunl .s-mnmm'izo m wrify that your nusm'r m {(1) is mum-r 55. l's'v thv smmrmrr'm mmnmml m mlt ulnfn 'rhv pvrrr'ntum' ()fh'mnlm. I'H (-itizvm. Bias-ks. um l-lispnl'liw: in thv sample. '1. U! 0. {Eric table to (it-~Hr'1'ilw the frv<1110110iu~s of Fenmlo, US citizvna. Bl-lf'k' and Him-mics in r119 s-ruuplc'. Now use the sort connnand: o What is the I'Ell'!' of rhr' highohf wage Wurkf'l' in the samplc'l' Wlm'r is i'hvir WK? 0 \"half is the lghvst (It'lumfim: lvw'l in \"(116' smuplv? 'Wlmr i. the ighvb'f wage' of tho llighvst (educatth pvrsnn in tho Haunplv? Now use the mmmzmd means wifh the option let:el(.9.9) to mnstruct 99' : mndm'u-p interval for thv mriablv wage. Is this narrower or wider than thr' 95% intvrval? er r119 mml'nand #156291} to tea? whl'ther the probai'lity of hving' a malt- is equal to the prob ability of being a fvnmlt' agnimt the r\\V('.)~.-.+id<-.~(.1 alfvn'mtivv that they 211w unequal as wall as against each 01m of fhv ()110-5id'i alumna-1tin Make HUIO fu fmmallv state your 111111 and lthf'l'llfin-B llYpOEhQH'h in each case. h'lterpre'r (".119 p Palm of yoln' test. wagggw Question 4: Consider a. continuous random vm'iabie X. whose prubahilitjv density function is given bv: ffr1:{ (cm ifngxgl 0 otherwise 1' Determine what. shnuid r be for x) to be a. proper prebabilitfr density: function mm} 2. Compute P{0.25 X 035} 3. Compute the mean of X1 4. Compute the variance 015 X. 7 V: W. =Q'u'cstlon 5:; ,1) Q LSuijp'S; X m- 312* 10) and 3' r- NH, 8) and X. 1' are independent- random variables. Emmi; is the distribution of II' = 2X +3"? XVI-mt arr: the mean and Variance of H"? .Iihcnmndlhg'rnn] nxpwtnrmn M Y giwn X. . in mlruintmi 3h fall-mm lat EyJ'JrLY = NY m an an E[Ea'x;.] U\"EmWW=mem- {-19 {SQLY =: .ri) Prul' : f\" / Cut-Minn '3') "gumdgr'fhv: {uuwmg Jain! diatributiuu of the Iamdum Rambler: X and 3'. I Campaltn thv marg'na] distribution of X7 } L9- 90 . \"hat is 110 Int-m: 01'. X? 3 \"11:1! in the: Variance u! X7 2'- Cumputa: the marginal disiributiun uf 1'. \"11.1! in tlw menu of 1'? (.1 Fr\" \"'lmt. Lu the Vuriancr uf Y'.' *I Computv tlu- diatrllnuiwn uf X ('tri'liiltiullal an 1' g 3 :54 Compute Ea); ' = 3) E? Lh'tvrnnm' whr'tlwr nr mt tho newlmn varlahlm X and }' are unipponrlvnt J llh'ij'K 5'01\": o'lh'f'l'. Qlltin 9.: Tu struldzu'dizp .1 vru'inhlr' 3m" in: aubiracl its mum and dividc: by it. btmxdard deviation eh! Iiztgrntp thr- arm holrwr two pnlf undf-r tlw nrrrumi dmtrlhllrm us! Add and tubular! 1'98 limt'a L110 stun-lard dm'ialiml to the Variable: NH rliw'dv 1f hr man Mandarrl riowminn. as law; as m: mmn is l I \" on)\" .__"_/l..'3_>_'79>(.5/I73>) H ,, ~_ 38,, '\\ 'T . . n O f 3 , Math and verbal EAT SCUI'EE are each NCBOG. 100003, 1. \"int fractiun of btudents scores above. YES in the math SAT? Abave 600'? Be- twccn 120 and 530'? Below 480'? Abate 53D? gc. If the math and Trerlial 5mm:- wore independently distributed. which is not the case. then What would be the distribution of the overall SAT scum? Find ites mean and imiam'e. 3. Next\" assume that the correlation coefcient between the math and verbal SCUI'Et: is 0315' Find the mean and variance 0f the resulting disbrib1.1tior1'~' . 4' Finally. assume that you had chosen 12:3 atuclunts at. random who had taken the SAT exam. Derive the distribution for their average mat-h SAT score. 'What is the probability.\" that. this average is above 5343? W'in it? this 50 much smaller than mur answer in (a)? 31-2: _ Question 10: Tr L14: f False If Explain 1' If X and Z arc two indupondent tandem Vill'liilJlQb, then l'ar'fX w Z} = Viz-riff) l'ariZ'; go If X N Kiting]. then Z 2 -- NEG, a] If X w 31:0, 5) and i" = 3 + BK then pxy = 1. If X ~A'f,13then Pill] X 1.645) = 8.10: 9'9"!\" If X and l\" are indepmideut- nuldom wu'iablea then the cunditiunal distribution of it" given .3," is just the marginal distributiun of i" G; The population t'm'arimm hctwcen twu mndam variables X and Z can be mm- putin as; Cough\