L4 - Sequence of Random Variables 3

L4 - Sequence of Random Variables 3 - Scavence «X Random...

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Unformatted text preview: Scavence «X Random Variables Ell: 145+ WNW” --- be. Mkpomlad' normlla 67:16th wa'k. mod) mfg. L94» x.=o; x“: 0.7 xH +w“ , «)1 Typical Sampie paths of X” and the empirical mean and vanance WEI 1ime Empirical pd! 01 Km 10- . 2000 Empirical Vanance = 5.26 a 1:0 19 - , == 1 .I 0.19 5 _ _ I - : 1500 Empirical mean=0 1000 500 4'0 60 so 100 Pm ‘— n 10 Dino’s .‘A Mud“ mefa) {X030 come/~39.- '1. Claim: XALXMN(0,V;3 w‘W‘fi 0’..=-6L‘-fix.5-263. ._.o , x‘=.1x°+w\ ... w! ~\N‘(o,\) 0.1X,+W,_ ~N(o,(o-q)‘-\+1) = 9.1 x: + W3 N m a, (9.1)‘[[9.1)‘+1]+I) x. X: X: 1. X“ N Wm, 03,") what. o':=(o.1)-ofil+l , n21 1 some, r} m»: when, 0': (on) Nah P( w 31) = p(w $1) ; 0.01 (ngm 7m)». \ 4 MM: ‘03“ Month? 2 CSBV PUXn-XMI >9.) >2 ?( XA.‘>,0,wflg—2)1~P(xn.,<o, wan) 3 1%!“ 903-?(w.$'a) ‘r ?(xn~)< 0) '?(NA)9‘) ) 0.92 Djha m above, not. i’Ux —xlzl)+ P(|x -x|z)) ; POM“), or m “I?! 13;; n M fl bowl > W Ixn-xn_,|>2-) 29.01 imam. We, MmfimvosekX-Mpnb. fl mos, X“?! X or 1.334 X. 51.3 Brawl”, w L «‘5' \uvg “‘0. “M5 hv. X «3' WM 1 is Aflwl} Na but“, we «m we m foan «Ham. Comma Crflax‘q «3.9;- (mvaBMce, 9; WA wn‘e‘der. '- For . number‘s % 3&— 6 wt Z753” ‘4 M Raill>0,mm)s =x. .9 [1- 1:04=)N<Io5wk§k+ erg-N14 t. #24409 n “M ’a‘.‘"|<g fan“ or)” ‘0 m—‘r x a: an; «.13 ¢ Gm flip-um l»,m-;g,.ml=°3>=l “"44” 3:) xng'x was. Efx‘14oo , :;f L». Ellxn-XM)I].O “IN-i“ Fad" ‘3 1M Efxnxm] = on (i.e.,mlm?exrsb lm Ann-fix. F flan—u. “‘4 n "m MW Elm-xx] = eixflrEer 342mm 4 o LimH- “Ravens 1s.- :.:.4. Sequence. 4 we,“ “macs CMW‘M fie- dnmchw‘sh‘cs 0;. S“ = XI+X11...+Xn mm (Law a; Large Nomde mm) 1.6+ “3}?” be. 504k “‘95” EM] :14 40° far cock 6.2m... fl Le-I- 5n; zx;. Then, 7:) a) 35—". i. for 8w: c<°°, who‘ve, VorCXDsc {walla}, n «J mvCX;,X')=a f" 139' gm“ b) (Weak. LLN) So 1, r r; thh... m 33,4, 0 06%?) 14.3%) 5112;]. xvxh... on m. ...
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L4 - Sequence of Random Variables 3 - Scavence «X Random...

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