Sim_Lec_2 - / K.“ Siwvlwh‘on (a, L pm bah“; Redraw '...

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Unformatted text preview: / K.“ Siwvlwh‘on (a, L pm bah“; Redraw ' C0“}: Las’r Ieofme we discussed: I) Random Variabkg . X3J1’9/IZ JLr-Jcke space 04f ou’rwmes. .Ho’gl— {mWth-we Marked J), 4‘0 unfit/5,1] EMS. Z)W€. saw example: [HEM (NP) Say n=3. lh Cage flsfidj x [01'] AEOI'J wen , w=(o.,oz,os) UI,UL,US UlBl'j N'S‘ Xian: 1(0. sp) + 1(Uzs10) + 1W; s10)- mfia Ofle‘n we dmp Hm coin £00) CMA juer om’ch. ’n EXM: :mnA()4—L), ' =an - WWW: Ms mama LS inema‘ewc kw we don": care abod- H‘ How. m mm m erfiez random variables. 0 Law (if (mg; @2231: H’ anz,... 0W9 lid W's such M {baby €C—ov,00) , W, , ‘ L . a r - @RCMMO; “00041) Cam‘ov’tt (@105ng value 0+ 6(DL{‘JX 'M m COYI‘HW’OUS Cm, {is X33 _7 A 7 {anmkam inm‘fiscwkcagc,h,0\L,-m‘7 ‘0’“ wives (D égexamgmz Suppose Z M CcH3 F(x)=IP(X$X—) =) :VZ H’(I")=‘/\4 =9 €X=li FP(1=5)='/v = qufi % 2 my @ka‘ doe: H16 UN saxfs in meHQM Define 30:16:19 Ua ow cad 'rvis unifl—OIIJ. and wnfc 3F ’/z~1(Uas'/z)+4-L(u; 6(92,‘/«])+5'1(Magma) UOHCQ W Since, COI'hJI('/z'5/~,J and (S/VMJ cue disjoin’r WWW/04$ , XL com onh/ Jrake he Values'lafip. By ams’rwoh‘on we haw, IP(XL=’U= n5 (means/1]): mm “’4 lPtXL=I> 3‘ U3 (UC€('/z,5la)=’/w the NIi-b 11> (XL-:5) = P (we (5A,, :3) a W WHO"). 50 in hated“: : A- cams‘PO“dj —i(file(51‘/L3H (5f(hlel'lz.5/QJ HS) é +0 ' amfld -) =l (MEG! V13: "2. CHALcUIu-WV] (MS 1 09m +0 =£th°W 6 Gina l"?- 1” {Alone 60/115/‘1 H15 ' OOGMSMA'S“) X- \000 (9 =SU‘M 5!: (000) 1000 Q; ’41“ Y up ""9 9M6 ’r‘nisis ’rhe, @OW- 0+ Monk Carlo: @remowk‘ \n We LL10 Mahave Want me. LimH— (03 n—no) \ 063 +0 0+ We fivewibth Fégif "(ammo 6;) I hon) [0638, In pmdricc wen we ‘ do we new +0 +a|<e 14 (+0 make, sum wail-w answer we calcqu is dose Gawak’w «3;? fins? USe (Lo/\er lim{+ weowem CCLT), 3W CCLT}. Suyposv. 'xuhlw cm c'c'd random vafiabxes wiw 6XL=re('w,ao)avxd V0\I‘(}('\)=V" <00 . The“ , 1P (@HZ‘,“ W“) )g—gg‘ Pmlouflk) When UM!) Cs no’rahmrfvc Dorm at (jaossrowx W wi’m mean Em and Vaficmcei. u; Enpbfl)‘ H‘ex‘ k Z Em = IP (29;) = JE-j€~M d5 -zz/z (Md densih/ finnon 1gm): fie , n / ' @155“ “N x z 2) JfiZchfl+§ng uvvaVVW 6m s‘to 01F ejlflorim “wit Carlo . '\ ‘ Y6 l x. _:__€YISU Cg V\ g; <- 9,“ < Cf:wa ‘ To Swm ’ =9 ‘ $ {KI-XL Q’./‘+%:2'<: WUACS . ww‘ame Sampw. N: indepwaw’fiy vhawf waeg , WW Cuzcaycww) M {92% dose 40 W expan (ooW‘ch (5. Wm we wank Jm mph) (3,) "\ K As we Sago, vaYTowme is an impofiuw‘c quanfih/ . loamy: [4’ new h) JMC WV 8n t'hc'mmh: Cmfio meBnoA. Rama, WM) = Q;( (X7011 IM=€EX, also 31113313, Var (X): €(f7’) ~(€(X))L Same pmmieg o_4r_ VafiaWCe. Lel- d be. a ems-punt X random UMCQHC. I] Var (al+X) =l/01r(X7 I L) , Var (0k) =0 2,) Var(o(X)= all/0M1) t1) Var (X4) = WINK) * VO‘I(Z) * zoov wheve, 00v (Xi) = @( ($151) (2" 651)) = m) — Ema!) . H 5) Var( 2:;Xa) = ZVaNXi) 1* Z.in (3,213). 9:. [six] 5n (*9 4 X51 arc endeperxdem N‘s. Men cox/(mm. Mowing (1+ he shiatch PYUCQSS is also Very imPcfl‘cmt (De, wan+ +0 build. simphe yek Pomvful mow, 7° 4,9 30 we mos+ awash“; the bufding blocks. Erica/(ll some, vaxpor’mn’r Simpha mews Saw— Snoth ‘Eexvxoolli ( Gaussian 2') Poisson MOdEJ 3') ‘0 Eda S) k— dwkribfiipn, ...
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Sim_Lec_2 - / K.“ Siwvlwh‘on (a, L pm bah“; Redraw '...

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