internship20120620195903481 - Nam-9i So{when S ECEn 370...

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Unformatted text preview: Nam-9i So {when S ECEn 370 Quiz 8 Firiday, March 2, 2012. TWO independent random variables, X and Y, are both given by a uniform random variable over the range 0 to 1. 1. (2 pts)F1nd the PDF for the random vanable Z, where Z = 5X + 2. Xe £3, {3 . L\ £0} a {r ,K cm x (I, em 0 of-MVWJA X: 2 'nz ( x —-- 5 F” F D JKK‘C I * t (F .Fxoi)‘: ID(KE it)? P(£g:?5 5".) X if 6- )1 un- l ,1 x >1 2 , , _ o 1'? 1‘22 1 l 3 q l; S 7 9 "$425) jam—{“3 #25257 If: a =>a=2 2. (4 pts) Suppose that B =maI(X,Y). Find the PDF for B. qu(z);dF-J1} 1/5 ”(2% I ’7 2 )7 1:3 1 :) 1:1 7 '5 a aflwyligz 5— ’ @(5)=P(Bst)=P(zsx)PCfsy) 1 =L1Jfar 05551 A“: 'f - h f {a}: QtJfarOMSi a - 0, aherw'se. 1/ / frat-‘61) 3. [4 pts) Suppose that. D = X—IY. Findfie/P/iéF’for D. O , Ln (LC-i --D//// , /‘ mm; prfcl): 1091);} {or 45450 6 ‘i l t x r _ 1 D I: I -] / ‘i / K Y . .. :- CL‘J'i) {or ‘15450 l’cl, 1Cor Ocdfi O, oiherwise. J gm: ...
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