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# midterm1 - a Q 2le 23630)” i233<§3i§1§5{£5...

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Unformatted text preview: _ a Q 2le 23630)”? i233<§3i§1§5 {£5} TVEU'EIEMK}: lMiidterm Exmn 'I‘UOSday; October 27 2007 Name WWWW ’ Scare Please do not turn this page until requested to do so. librehlern it ’20 ptsjr Let 2‘5"} :12: (XhX X1) he four munhers in the range {125374} "l‘hese numbers are drawn from some unknown joint distill)ution5 however it is lmown that the rulinhers are {listinet wii‘tl'r probability l. 62 {live an upper hound on H/(X‘l) that can. he ael’neverl by some distrihutiorn and identify tl’rat distril‘rution. 0 Your friend John observes the value of X 4 and you ask him a series of questions with ternary answers (i.e., there are three possible answers ABC to each question) to deter—~ mine the value of X 4. What is the maximum possible number of questions you need to ask? 5: ‘ 5 ' :11 , 82155 p17<1<3511<15y 2‘30 11"‘1521‘5111‘1 05551555 is S5105)C(5 51.1 a 3701‘“: 5111111111 storage 2111011: .: ., :1 ‘1 a) 1 51 \101 3/<521.yg 5572115711132; (111 Sopt<111151<111 5., the 5055031751112; operation .51; 3’):3.1‘5<)1:111<1<5: <5 551121131 :1 binary 11:11.1:501’1‘1 171-1115215150, X 573555351 551115: 71(X :22: {51111) 55555 52/ 5 £1511: 115 5 :1“: 5) :: 2/3; 5 55: X ***** 5} 101110310. 5/2 05510. 512155: 510111 5151:) 1:101 (111:1 111021 <5 55 X :7: 5,1, 1'01110‘3/5 3/15: 05 the 112155; 510111 the storage 21113021,. 8(111161 daya (1.11.537 4 011 fewer grailm W555 :1011'121511 511 the storage area: Your friends: A1111, 5305) and 05515110 pre< 55053 this event 3231155 occur 011 Sep5LG51’J.bCI‘ 207 80111011153611 2451, 1:111:55 October 5:11, 195555005 we] 32 51557511051 0110(1: ) 05 55168:) three predictions 1115115515 11:10:55 5361186 and Why? /\ ” ”M” “W W 5 5 :51 5/5»: 5.55:5 : \$53555} ...... 55551555551115: {WY/1556 55151:: .:~3 111311155 515 110 1131-1 1 1 :9 5511:.) 5511/?“ 035/11 5150525: 510 5! {WV/755555955“ :9 15:51:15 "‘ 5 55111521 “”1" “-55 C @2105) Pmybﬁeegm 3 :20 p113]. Let .qu 2:: O and, X71“, 7) f5: 1 be a, I\Kffarkov drain with i;'1:an:31tjio:n_ pmbabiﬁties p(X7-,Jl,1 2:: IIXY: : ) :2: [)(ii’im‘IMj 2:: 01X; :- 1) 21 Véflmt is; the QIIJiIiI‘Opy late of 'iuhiss procesg'? , 3 i, L”; » 2 m z . ,(Zm WK 1: my ' <i,f5£«.,<ziy~. wk, (/9wa "{7} 9 ﬂ 6 W3 WEIQLWQQ ittirobierr'r (i [10 pt?) A random. variable X is drawn. airing value (117071) with reepeetiive pro|:>a.bi:litiee 2/5., 2 J n /57 and, 1/5. You are asked to guese the value of X and make the re; smabie prediction that r 2:: (1.. e:- What is the probabihty that your guess its eorreet? } ea Now a friend reveaie to you that J} :75- 0. Should you change your guess to X 2:: Z)? If you. do. wl'iat is the probability that your new guess is correct? Problem 5 [10 pts]. Construct a Huffman code for the following probability distribution: p r: (.1, .2, .2, .2, .3). piﬁ'iﬁ‘giﬂéfﬂfﬂ ﬁ [20 p181” 'Ehc sequence x :2: 1000 i3; (lifamx from the ﬁd fi<mj1<m_.l,li distrihu 12km wiih "}‘<11"m}1(‘/i7€)1” '1 I ;~,~-;—_ {NJ [35.11 2:11'ithmc‘t,:i(i coder is; 1189.6 1'30 encode )1. Give the, 011173111: (xxiewol'd, .i . < ) or J “ “ :éwwiil‘am (75:: < €‘~é19?i7“‘“W{/W”‘ ...
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