quiz6a - Math 3101 (Fall 2010) Name: Quiz #6 1. Let X and Y...

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Unformatted text preview: Math 3101 (Fall 2010) Name: Quiz #6 1. Let X and Y have this joint distribution: (a) Compute the expectations E(X) and Y) ’a d tile vaiienoes VaT(X) and Vera”). 5M3Mfl23 +2'.3 #47 g{y):0°.2+ HZ +32% + 4 '. 3 5‘ ,Z—raéi' /-2=E /- E/A’Z)=__/2V./‘I/:"/ '. 3+4} ‘ ,3+/.2 : /.§' %W{X): [vs—m" 6N2: E/W-.2+4-.3+/623 =.2+/~2¢—4,g: 42 Mar/7): 602-222 = (b) Compute the covariance 007) (X , Y). 1m: 7) -—-— m7) - Hem) : {2233+ 2/5)?“ X “'- 11.? ‘7 2. Let X be a random variable with density l 2 l 2 3 = MN.” 35' a y a fxtv) { 0 otherwise I E '7 Z L i f J“ “9 (Db-<1? We“! dost :3 xc’w) _ «H—l ....__. X4” Xvi; 6 J’Nrrwhlcl Sulfa; £535) 3. Suppose X and Y are independent random variables with expectations E (X) = 1, E(Y) : 2, and second moments E(X2) = 2, E (Y2) = 5. Compute the expectation E ((X + Y)2). anew} =F/X 3— 2X7 + 72) : E/XZ’H JEWEL-79’) + Eff?) :39. 1.24.5: m .g€¢ Of é‘c‘pé(/JL'L ‘ipMQ d ...
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This note was uploaded on 01/03/2012 for the course MATH 310-1 taught by Professor Sarver during the Spring '11 term at Northwestern.

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quiz6a - Math 3101 (Fall 2010) Name: Quiz #6 1. Let X and Y...

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