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3. (25 pts.) Let X1, X2, X3 be independent random variables such that Xi~ Poisson (A), i 1,2,3. Let N = X1 + X2+X3. (a) What

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Xi Poiscion CdD, is i,21 3 mgfmi)-di cet-) Given NX+ X tX CE MNIE-Mxitxz+ X3 are independent e ا0ءاء( __ َ(ا*ه- ) Timpiesthatndependent are n--! -(AA +A) C*-K+メ+Xg Poissfon Cditdstde)] CA, +dt n-x1- Xt +3 (n--%)! +3=n CA 23! P+p+r -n-7, 2 P. iF2, 3t ond rnomial C N, P, P,P3) Hence C , 3N) Given Cx lN)~ rinOmlat PC 3N): N, P, P,P3) P. P. P P(N=n) -(+st3) (astaz+d2) 7,13!d3 1 01 2 2 メ3) PCYメ ence (4 ds), d

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3. (25 pts.) Let X1, X2, X3 be independent random variables such that Xi~ Poisson (A), i 1,2,3. Let N = X1 + X2+X3. (a)...
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