Functionsof discreterandomvectorsSuppose that(X, Y)～P(X=Xi, Y=yi)=pj， i, j=1, 2, ...then Z=g(X, Y)～P[Z=zk}==pk,k=1, 2, ...(X,Y)(X1,y1)(X1,y2)(Xi,y)orpijPijip11P12Z=g(X,Y)g(x1,y1)g(X,y2)g(Xi;,y)
Functions of discrete random vectors Suppose that (X, Y)～P(X＝xi, Y＝yj)＝pij ，i, j＝1, 2, . then Z＝g(X, Y)～P{Z＝zk}＝ ＝pk , k＝1, 2, . (X,Y) (x1 ,y1 ) (x1 ,y2 ) . (xi,yj) . pij p11 p12 pij Z=g(X,Y) g(x1 ,y1 ) g(x1 ,y2 ) g(xi,yj) or
EX Suppose that X and Y are independent,and thepmfs of X and Y areFind the pmf of Z-X+Y.Solution Because X and Y are independent, so
EX Suppose that X and Y are independent, and the pmfs of X and Y are Find the pmf of Z=X+Y. Solution Because X and Y are independent, so
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EX Suppose that X and Y are independentand both are uniformly distributed on O-1with lawX110PpqTry to determine the distribution law of(1) W = X + Y ; (2) V = max(X, Y) ;(3) U = min(X, Y);(4)The joint distribution law of w and V
EX Suppose that X and Y are independent and both are uniformly distributed on 0-1 with law X 0 1 P q p Try to determine the distribution law of (1)W＝X＋Y ; (2) V＝max(X, Y)； (3) U＝min(X, Y); (4)The joint distribution law of w and V
(1,0)(1,1)(X,Y)(0,0)(0,1)pij20W=X+Y11V=max(X, Y)0111U= min(X, Y)0001W012?000I0
(X,Y) (0,0) (0,1) (1,0) (1,1) pij W＝X＋Y V＝max(X, Y) U＝min(X, Y) 0 1 1 2 0 1 1 1 0 0 0 1 V W0 1 0 1 2 0 0 0