# ECO320-test1A-F11 - /If,~!< Name Section ECO 320 Please...

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/If,~!< ECO 320 Fall2011 Test #1A Section Name . ______________________ __ ( Please print ) Show all of your work. The # in ( ) in front of each question is the point value of that question. (29) 1. The random variable X has the following p.d.f. f(x) = X+ 1 X= Q, 1~ 2, 3 10 = 0 elsewhere and A = { x; 0 < x :::; 2 } , and B = { x ; 2 :::; x :::; 3 }, find (6)a. F(x), the distribution function of X f( x) ::: () xLO flfJ :::- ~ 0 ~ }( tt_l :::. ftllioJ £ >(<::2 :. fo:l ~ )(L'J ::..JQ.. ?LX' to-1 ) - (4)b. Pr(X:::; 2) 1 - ) ( 4 )c. Pr( X -:t 2) ·~fr(t-(X=.1)) ~ 1-1 ~ ]_ tv to ( 6)d. J.l, the mean of X '2t -;[ 'K -fix) 1t:::. o-ffo)-+ t·fCr)-4 gt:t;)) , .... + ?.fCs) 0+ .1. -f._.. -t fJ.._1o ..... l ' (.? tc) TJ -(J - (3)e. P( A u B ) " -to (3)f. P( An B) -l (3)g. P(AjB) ~ ~.Jt.t;\ 1-.. ,.,_n. VdV ~ ((5 v ,~ u t) 1--e-~\.- -- , 7 f_C~PJ) 2. : - :. / 7 [fit g)~ - -:. w · c" pus) 1 1o _ ~ --- 71') 1
(30)2. An urn contains 6 red and 3 blue balls. Let Ri be the event the i -th balls drawn at random is red. If the balls are drawn without replacement, find (3)a. P( R 2 ) ;:. " {' (3)b.