P(X=-1)=P(X1X4=0,X2X3=1)=P(X1X4=0)·P(X2X3=1) 0.84×0.16=0.1344 P(X=0)=P(X1X4=0,X2X3=0)P(X1X4=1,X2X3=1) P(X1X4=0)·P(X2X3=0)P(X1X4=1)·P(X2X3=1) =0.84×0.84+0.16×0.16=0.7312 P(X=1)=P(X1X4=1,x2X3=0)=P(X1X4=1)P(X2X3=0) =0.84×0.16=0.1344 X 0.1344 0.73120.1344 3.设二维随机向量(X,Y)服从矩形区域D={(x,y)0≤x≤2.0≤y≤} 上的均匀分布,且 Jo, XsY; 、j0,X≤2y; 1,X>Y 1x>2Y 求U与V的联合概率分布。 解依题(U,V)的概率分布为 PV=0"=0)=P(X≤Y,X21)=P(xY)=[小 P(U=0,V=1)=P(X≤Y,X>21)=0; P=1=0=Px>yx2)=P<X52)=4= PV=L==1-P=0=0)-P=0r=)-PU=1=0)= Y 4.求习题2.1第4,5,6题中(x,Y)的联合分布函数 解(习题21第4题)30 0.84 0.16 0.1344 ( 1) ( 0, 1) ( 0) ( 1) 1 4 2 3 1 4 2 3 =  = = − = = = = =  = P X P X X X X P X X P X X 0.84 . 4 0.16 0.16 0.7312 ( 0) ( ) ( ) ( ) ( ) ( 0, ) ( , 1) 1 4 2 3 1 4 2 3 1 4 2 3 1 4 2 3   = = =  = =  = = = = = = = ＝ ０８＋ ０＋ １ １ ０ ０＋ １ P X X P X X P X X P X X P X P X X X X P X X X X 0.84 0.16 0.1344 ( 1) ( 1, 0) ( 1) ( 0) 1 4 2 3 1 4 2 3 =  = = = = = = =  = P X P X X X X P X X P X X 即 3. 设二维随机向量 (X,Y) 服从矩形区域 D = (x, y) 0  x  2,0  y 1 上的均匀分布，且      = 1, . 0, ; X Y X Y U      = 1, 2 . 0, 2 ; X Y X Y V 求 U 与 V 的联合概率分布。 解 依题 (U,V) 的概率分布为 4 1 2 1 ( 0, 0) ( , 2 ) ( ) 1 1 0 = = =   =  = =  x P U V P X Y X Y P X Y dx dy ； P(U = 0,V = 1) = P(X  Y, X  2Y) = 0 ； 4 1 2 1 ( 1, 0) ( , 2 ) ( 2 ) 1 2 0 = = =   =   = =   y y P U V P X Y X Y P Y X Y dy dy ； 2 1 P(U = 1,V = 1) = 1− P(U = 0,V = 0) − P(U = 0,V = 1) − P(U = 1,V = 0) = . 即 Y X 0 1 0 4 1 0 1 4 1 2 1 4.求习题 2.1 第 4，5，6 题中 (X,Y) 的联合分布函数。 解 （习题 2.1 第 4 题） X P -1 0 1 0.1344 0.7312 0.1344