Show all work in detail or your answer will not

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Show all work in detail or your answer will not receive credit. Write neatly and box all answers. No calculators, books, notes, PDA's, or cell-phones are allowed. Answer the questions in the spaces provided on the question sheets. If you run out of room for an answer, continue on the back of the page. .. Do not Wie your own scratclJ paper. Extra scratclJ paper is available- from the front of the room. Question Points Score 1 10 ...... ", d~ 2 10 U 3 ).0 '3 4 ,10 rO 5 10 IV 6 10 '0 1 10 ~ Total: 10 53 (''''I ,'···1· .... " 1. (10 points) Roll a fair die twice. Let X be the random variable that gives the maximum of the two numbe .... Find the probablility mass function describing the distribution of X. ~ ~ Lf i <; ,p 1\ "" YY\C\X O-f -I'U +w 0 nuty\. \::> ~ ~ S 2 "$ '-i $ \: .. .-.--_._------_. - -~- x X x: )I"" x.. 'f. K. )( I' '" ;I. i- >C. X SCL\YtyV S,'H 3~ X X ;;< " x 'j" H ~ .? \ ):;:. lp~ \<> 1f'(:,X ? 2-) ,,-. '5/ 3 (p P( X ? 3) ~ 4;3\0 i) l'v > q) ,.:: ~/ I ." ,_. . 3~ \? ('f. ? 5') '-. ':l;7 31p ,rex. ?:..4» \/~1D "0.: ..... ' ... I'
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----- ----- --- r t 2. (10 points) Suppose that X is a discrete ra.ndomvariable with the following cumulative distribution function .. 0 z < 2 1 .1 2 < x < 3 F(z) = .3 3 ~ z < 5 .7 5~z<6 1 z ~ 6 Calculate the variance of X. ,'I\A.,.X" ..:~ I 0, \ \ ::;> :l. 2 .) \ 0,'].. , il S 'O,1t I \ \1,'1 le' ,,>- \p 1i)·3 \ l' 4 - \)" V/ Q , "' / tv' Lex \0 r; LiC') - \f 1-. \; L 2,6 .. r;.Q \)(1'\ ex,) ~'2t Y- - r )2.? Lt."'-, r..,) " 'lA.'\P ~ I 0 -:'J~';:'~!:~ rc \ ' ,i 1,\·\\0 <> \ ,'3'-1 ell.= (2)(0.\) -\ U3XD,t) + ~)((),4)\ 1,:\0.:») ,V.;:; / >{} ? ,() .".- '\...Y "',) 0.7 -t" 0. \.,.\ 2-.0 -+ l,'b '3 :~ '2, .,.1>, " 0.10 ~) LL \P '1' It ~, Z. ., ....... ----~_. (1)'(l).\)'\ (·3)2..(O.~)-\ l'=:/)(~,4)1l~)210;~ ii' ~ r f..-' '2, 2 f-'~ ~ :, -- L.t l iJ. \) ., 'q t b. Z ) ~ '] S 1.. () ,"1) -1 .~ (, lo .', 'J c),1; DV o ':+ \ l, % ·t 10 0 10 + t O.l> cc.y 2. -3 , 0 I C,O I '3\0 '"' /).3 ~\~/'.J:). If'" If OA LX-.I : Ex:' - (p .. y" (lo --,/ 2'3,0- L"h\O)' ::~;;,>'" -"'\ f()~ 'Y '~ Q t02 ;,\-,' -=/?-'3,D- 2\,\\; 2(; 2 - " 1.8 ~) ~~ 'iT'L, ,Q.:.J 3. (10 points) Suppore that X a.nd Y ace discrete ra.ndom variables with the following joint distribution X-I X-2 X-3 Y-l .1 0 .1 Y -2 0 .1 .3 Y -3 .2 0 .2 Calculate E(XY) (the expectation of the
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