Quiz2sol - BB 178 Handout#20 Prof Abbas El Gamal March 6...

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Unformatted text preview: BB 178 Handout #20 Prof. Abbas El Gamal March 6, 2008 Pop Quiz #2 This is a 15 minute closed everything quiz. The total number of points is 12. Partial credit will be given only to problem 2 (so you need to show your work only for problem 2). NAME: 55 \U 5x; MS 1. (6 points) Label each of the following statements with =, g, 2 or NONE. Label a statement with = if equality always holds. Label a statement with 2 or 3 if strict inequality is possible. If no such equality or inequality holds in general, label the statement as NONE. (a) (2 points) E(X3|X1, X2) vs. E(X3lX2) if X1 and X3 are conditionally independent given X2. Answer: l .——» l (b) (4 pointS) Var(X) vs. Z?=1P(X E A,)Var(X|A,) if £11,142, . . . ,An are disjoint, X3221 P(X 6 A1) = 1, and E(X) = 0. Answer: \/M((K\? E(¥1),E(X3L - : C(p} simc 650:0 Z, Lh’l’fll :% v mm : (wa > ””21“de 2. (6points) Cameras 2 :% \9(X€A lVWPfil \A > VWl“ 05 Em») Alice has 10 cameras in a box. Each‘ time she goes on vacation, she picks up one of the cameras at random and takes it with her. When she goes back home, she puts the camera back in the box. If she went on vacation 20 times during a particular period, what is the expected number of cameras that were never used? Answer: M-LWW‘ 0£TW0ll(ah/J f/U‘lem AL: %\ \Wmmara kiSVlQVIIUVd O ‘olw it 0: Cow‘mi WWW! ugffl‘: \i; AL L>l it» _ dfibecowaswwwyw : EC? AL) ; ‘44 (AL) «Wt k3 ,0 (Ira/He t)! not \:\ 10 ulflfivfld QQCV‘hfl‘Q' WW?” 5 l0 (fi> :\l 2 l U 301nm“ /” ...
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