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Unformatted text preview: S O L U l J Math351 Spring 2010 Exam 4 (1) (35 points) Bails numbered 1,2,3 are randomly placed into urns numbered
1,2,3,4,5 (each bail, independently from other balls. is equally likely to get into each of the urns). For i = 1..5, let Xi be the number of balls in the ith urn. Find
the following:1 3 : “HM. W ‘ (1) P{be11 3 goes to urn 4} 0—? M or was (2) P{exa.ctly 2 balls go to urn 4}
(3) The probability mass function of X4
(4) ElYl (5) El: Xi] m J? h
< l 3 Ll? EL : 0.0%
(2)3; 5— :05“ 1 r y 3i
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EULIFPWFQZPEXLrol, 5.) 1In this problem, the answer in the form of a. formula, such as % is OK. L 6
mEUJ=S lrﬁdﬁd" 3 (2) (40 points) The pair of random variables (X , Y) is uni rmly distributed in the
triangle ABC shown in the picture. This means that th joint density of X and Y IS
—1 hen0<x<6 6—2:< <6 = 18 W ’ 3’
fx’y(x'y) { 0 outside the triangle. Find the following:2
(1) Ele
(2) EIXIY =21
(3mm Y) é o é—x ,
Lgilolx :é—v—z
VT: Sx(g(g—ﬂ)olx_‘ga
o 00
(z) 85KB)“: llmh’lloh °° Mtg/m o<5¢bw
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j lxa (1’2)
% (992): W
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E£Xw:l]: Sac §x]3(ac230lx 2In this problem, please give the numerical answer in the decimal form. ECU]:‘1 5;] 55WJ e e
giyﬂjjj ﬁxat—gaiadi
é 7EOgaxZ c,
J :ﬁix 6'(:X) 4x1§gi(121_x3)4x:
é‘ " 
:3‘302 2“‘%">“§ r Cox/(>93) : Elma}— E1X1~Eiﬂ=l§et1+l : \ ...
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 Spring '08
 Moumen,F
 Probability theory, probability density function, Randomness, Probability mass function

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