Q3_Math308_608

Q3_Math308_608 - Quiz 3 Math 3OSI608, February 5 1....

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Unformatted text preview: Quiz 3 Math 3OSI608, February 5 1. Consider simple random samplingL with replacemient. a. Is 1 " a n :1- 209: W X) k=1 an unbiased estimate of a“ = Var(X)? Suggest unbiased if not. b. Is 2 n N (n -- I? 20;" " XV =1 an unbiased estimate of 0% = Van-(T), where T = N X ? Suggest unbiased ifnot. 2. Suppose we have a. random sample X1, X 2, X3 from a. population with density f(2) = 1/9, a: 6 [0,9], 9 > 0. Find the distribution of X9), where X0) = mm{X1.X2.Xs}- \ 7kg Um‘a‘wxjcé n/QM‘A‘EJQ n " -—-Z ~_ _L n L_ “E + Z X D: -E(h-l(§=tx‘ ZX‘WX‘ "" .. I q 1- ",q-i—rniz)‘: #EQ-fifl (if-“Xv: 8X h -—--'2 :2 fl 1-— XZ“ {\X ) t l: h_ E; ,( )fl : _L\ ngxp—nELX»= h”— :1 .L ‘L —-" ) I: _ -~. Kg @xg)+vng@——Y\KEW+V04") i h—‘\ -_:{ L .# ,1 E -Z+<>")*“q«"+%‘ ‘- " h'-\ K=| 1A : KL! 9K+h6 —7I-<(—< >=51l k“ Q. ELI £KXK"->_()L‘I5 cm UghLJ‘IQSLA canaco‘t De «2' _ (fl ‘ n L L '1. "\ .— L a“ N2 _L_ E Xflli ail-fl 6 11-" BET)?” ElKXK#X)>-;I Et'flwslt ( )) h 1 . 'L. : h £61,: Eli-6'; Le, Lxusfié eSH'fiQ‘k “£51— ‘fi:\'n/ 5‘1th 2. IV #‘ n \ . / h~l n MCL ‘ I Z __ _: ___ 6'1} aVa/[T)¢‘/O~(va)zy W Z; k eri )L . I )(a) x} q/Q tnégtxnéerH' fifon 0x pofnlome ) \ Afivq “"J’L‘ °ltm+7 fix”; oceLg‘BB A 9 ,_E,——— o o’r’vuwif: C: e 5‘ ZQJ‘ Xk’b): max ix') )(‘3/ XJB / “Km ‘H‘L Qéfi of X”) / 55th Km) ts maxlmq‘ & < ‘3 1: Kat) ’5 PCXLSFDQT" PKXI S1) X‘sag X33“ :0 Km 3’ ._. (x.sx>P(xls>c>PkX3s1)=[F‘1’3 finch \méW’mé‘eM-L X 0 ,1 a; ’ O NW2. F991 ::[q,93 T q £ Le ’( 1 x>© 3C) =3 '5‘ = / :Eac :- 3 Wait 3 éiwkv’s (flab <> b) _ jxebBG) _ v Q Q‘PHMMLK fix ‘1) a L m ...
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Q3_Math308_608 - Quiz 3 Math 3OSI608, February 5 1....

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