hw7_sol - flofiéfim‘i PQX=D=D “.3: {911:2} =0...

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Unformatted text preview: flofiéfim‘i PQX=D=D “.3: {911:2} =0 '9..— W‘: PU=3)-:P PLX=0):3F D,3+0.L+P+3P “4—15 in? P: Dug :1 D. Li ‘7' PC i=3): $42.: PLX-fn}: 0‘37? EEK} atom a. 01mm Asmazom vaév/e- X :2: Make. is. hurt aw I'REW. PmHe.m-2.. PCH)=P , PCT): 1-P- bef X be.» fine.» Random VW'M/e.’ dewafifmg Hm MUHAva {9-4, flips {AT/[Hf {Liza-Lem hwds aw +m‘k ham atcmefd Wha- HWJ W 75:75 can 061cm f‘wr‘ta fr: +m fifanl‘mfi Sag/WA «3% 70,72; amid! X Sewuwtxa- PMBMBHH! :2- H, H (P )L L '2— ‘T, T' G? P) 3 H,T,H Flu—p) 3 H )T; T— PCP-"P91 5 T; HL—lj (1—43) P11 3 T: HM Par-P) PROMEM 3 LOU EEK] 300M :91 cwti‘mwwfi Rawaiam Var ithg, (Shaw E135] '2. m j —§ 0?"!— cl a 6%.) 1 == 4" 90 2 mare» i3 +00 D ‘ I:— D *5"; w M m, E“O)+Lf(x-—#e “J a: t”- L D u'E-x- W “Hm +2— .2: Ci) in m: am ' EIXE] ) pkg — WWW: Note is = 0 term does not contribute to 511111. n “r! a n—k 2 km? (1 — P) 35:] n (n _ 1)! k—l —J: = up -—-+--— 1- ” letk’=k—l 3;; {k — 1]I(n a HIP ( 3’) n-l (n ‘— k’ n-l—rk’ — “1’ 0'” surn cf Binomial probe with parameter n — 1 and p = up .I" F ,. Z k2 mpkfl — p)“'k cancelling; I: and letting k“ = t: — 1 II E ‘13 M” II H ’E + |-—" “~_.-* w“""""'*-. 33 3'": l H expected value of Binemial 1 with parameters in -— 1 and p flP{(”—1)P+1} ‘73: = 5IX21- 5W]: = npfin —1}P+1-HP} = “PU -P) 5) SlX]=/1m(l—(1—j;))dzzimédmzlnm —: on 1 H 1 w I; d a) fix] = f-mIrr(1-|—:r3)d$+jn rr(1+:r”) I: Consider the letter term: 1‘ 1n 1 + fy I dz=iln(l+mg) 2: [2 y)—~+m a 1r(1 + 3*) 2w {1 1r k€_a ! mm = ire“ k ic=0 = bcafu~1jl 8) a) Net reward Y = {1X2 + bX — nd, where X is a binomial RV. E[Y] = maxi] + bE[X] -— rid = e(E2[X] + Var + bE[X] -— nd = remap: + npq) + Imp - nd b)}’=ax E[Y] = flux] = E ( 2 ) (WWI -P)“"‘ k: = (“P+(1_Pi)n = ($+L)i-$£ EENJat ij= Z PU.) EENet Pwt/lfl {=49 mum” am] is. +an mpecmafi mméw 42% Uw't'fé Diogm ~ 0 O J I 5-D“ J iJflij-ri); hépcib Problem 10 b) but 707(10105 {but quncrbr'w $1 9‘ waaé firtv- WE?!“ mfim fl mutt .10 I'“ awfl x: Eava gymmeifi? 97’- Jch’ (—3") a” j fxbfi) 0b; 5 "[5,. "‘90 ...
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This note was uploaded on 09/14/2010 for the course ECE 302 taught by Professor Gelfand during the Spring '08 term at Purdue University-West Lafayette.

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hw7_sol - flofiéfim‘i PQX=D=D “.3: {911:2} =0...

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