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# exam4solution - S O L U l J Math351 Spring 2010 Exam 4(1(35...

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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 “9 WWW-ea oxalate) we: Pl «— )‘\O.3£& \t [I y’fjl {I'M-w?! L6 wrj 001:!” L:] g ) p l— [O M, db new”); _ 5L3 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 \ ._ 51‘ (21' E‘q j lxa (1’2) % (992): W >09 lgfl) (>0 E£Xw:l]: Sac §x]3(ac|230lx 2In this problem, please give the numerical answer in the decimal form. ECU]:‘1 5;] 55WJ e e giyﬂjjj ﬁxat—g-aiadi 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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