# ECO320-test1B-F11 - Name ECO 320 Section Please print Fall...

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ECO 320 Fall 2011 Test #lB 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 = 0, 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 r(x)= o J )(~ o J, 0 ~x~l ;J.. I~ "><L 2 10 1 - ~ :;1;. )(L J lv \ I , x::z3 (4)b. Pr(X ~ 2) -{'{ 0/ .f{{l)+fbJ:: I + :Z, ? " (p T.? -+'It -:. ((J ( 4 )c. Pr( X :;t 2) -F(o)+{{ I) rf{J)= fo ( 6)d. )l, the mean of X Jl~ o.f(p)+ /'fC/) + )-ff2)-+ 7-Ptl) = <9 -I- _2 + _Q .+ ,, ~ .02 ..... 2 "' {.;) To - /.!J - (3 )e. P( A u B ) (3)f. P( A n B ) (3)g. P( AI B ) f /.D _, 3o ? . ~- ....... -~ v ~ 1 1
(30)2. An urn contains 6 red and 4 blue balls. Let Ri be the event the i -th balls drawn at random is red. If the balls are drawn without replacement, find "'§ :: _h (3)a. P( R2) ::-Jff l ~ ~ - - (3)b. P( R2i R1 ) _. ~ f>(MB) f( ,1 /8b- f"Cf!J f' ( /1()8)-- p { fJ). f{ 8111)