internship20120620200220077

# internship20120620200220077 - Name Daﬂlﬂ-l{5-900 ECEn...

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Unformatted text preview: Name: Daﬂlﬂ-l {5-900 ECEn 370 @ Quiz 9 Friday, March 9, 2012. Yf‘i V“: ‘/a w 7: r! l]: . - l . ' . n_ _ a &quot;. Suppose I have four equally likely points (@551)’ (J, Q)1 (1,11), and [2, D). 51*] = V1“ A Z (___l, 532] ’ l . l&quot; l 1; fl; 1. (3 pts) What is the correlation coefﬁcient between X and Y? ° HIV] 1 l/2 ’2 + h 3“?“ 35-144 0 :t 1/2 1 X 37 c0U( .Y) couijygt): HEW] _ EDEEEYJ n. yq _. 1.1/1 1 _1/2 lUW(5L)~w(Y) H wit? REM-(W3): 5” LL ~. “'FL 2 F m &quot; ”’2‘!“ ‘/= ‘1&quot;:- N ? i I/oa U {‘3} x _ (Vi): ., v“! ..l y lé-l/H’l/f 2. (2 pts) What is the linear minimum mean square estimator (LMMSE) for _}_&quot;_ given 11', Y = E [Y].+ p5:— (X — E [X ]) A V*‘ 6-=J?ro¢ 137/“? &quot;/z*(*ﬁj%&gt;(x-l) 4. “l 2 6k. = tome-‘0‘) 1 57?: ' : V1 ' X + l —* x W «if; 3. {2 pts) What is the minimum mean square estimator (MMSE) for Y given X, 37' = E [Y|X]? \I l A Y 2 l 31&quot; x=0 m t”. [at :r x ‘-J '/L ...»... ”...—.15;— x 0 r*&quot; r&quot; 2 &quot;n ‘l G&quot; (0,0 T {pal . a \'/ __fT&quot;&quot;'(z.o) 4. (Zpts) What is the expected error, E [9 — Y] , for the MMSE in this problem? 72 - (+0.; -05) :o \/ 5. (1 pt). Is the MMSE in this case better than the LMMSE? Justify. __f X \lis , ‘ylAL mfnlfhum MP1 Elam/e. Lil‘fhwr 7; given?! 9 Mr es'l-vhw-ror. l’l‘ n—‘l‘ luxsi m/l'l‘avhj Jaw-J. all Finn. Fw‘rv‘h} ...
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