1、C?C?3.4C?u“O?VIIC?C?C?8IX?,Y=f(X)?(X,Y)?,Z=g(X,Y)?X=(X1,Xn)?,Y=(h1(X1,Xn),hm(X1,Xn)?u“O?VIIC?C?C?SN1C?2?l/Y/?3C?u“O?VIIC?C?C?SN1C?2?l/Y/?3C?u“O?VIIC?C?C?SN1C?2?l/Y/?3C?u“O?VIIC?C?C?C?8?:CX?,Y=f(X)?,fR?R?.u“O?VIIC?C?C?y R,Y y=f(X)y=X Dy,Dy=x:f(x)y.b?fNO,KDy=x:f(x)y=x:x f1(y),uY?FY(y)=P(Y y)=P(X Dy)=P
2、(X f1(y)=FX(f1(y).u“O?VIIC?C?C?y R,Y y=f(X)y=X Dy,Dy=x:f(x)y.b?fNO,KDy=x:f(x)y=x:x f1(y),uY?FY(y)=P(Y y)=P(X Dy)=P(X f1(y)=FX(f1(y).u“O?VIIC?C?C?y R,Y y=f(X)y=X Dy,Dy=x:f(x)y.b?fNO,KDy=x:f(x)y=x:x f1(y),uY?FY(y)=P(Y y)=P(X Dy)=P(X f1(y)=FX(f1(y).u“O?VIIC?C?C?n1CXk?pk,k=1,2,.(l/)VpX(x)(Y/),KY=f(X)?FY
3、(y)=PxkDypk,l/,ZDypX(x)dx,Y/.u“O?VIIC?C?C?1?CXkVpX(x)=2x,0 x 1,0,.CY=3X2+5?.u“O?VIIC?C?C?):?y R,PDy=x R:3x2+5 y,KDy(0,1)=,y 5,0,ry 53,5 y 8,(0,1),y 8.u,Y=3X2+5?FY(y)=P(Y y)=P(3X2+5 y)=P(X Dy)=ZDypX(x)dx=ZDy(0,1)2xdx=0,y 5,Zy5302xdx,5 y 8,1,y 8=0,y 5,y 53,5 y 8,1,y 8.?Yl!U(5,8).u“O?VIIC?C?C?2?CXlIO?N
4、(0,1),CY=X2?.u“O?VIIC?C?C?):?Y=X2?FY(y),KFY(y)=P(Y y)=P(X2 y)=P(|X|y),y 0,0,y 0=(y)(y),y 0,0,y 0=2(y)1,y 0,0,y 0,0,y 0=(y)/y,y 0,0,y 0=(1/2)1/2(1/2)y1/21ey/2,y 0,0,y 0.(t)=12et2/2IO?V.Gamma?V?/,YlGammaGa(1/2,1/2),=gd1?k2(1).u“O?VIIC?C?C?/,Y?VpY(y)=dFY(y)dy=ddy?2(y)1?,y 0,0,y 0=(y)/y,y 0,0,y 0=(1/2)1
5、/2(1/2)y1/21ey/2,y 0,0,y 0.(t)=12et2/2IO?V.Gamma?V?/,YlGammaGa(1/2,1/2),=gd1?k2(1).u“O?VIIC?C?C?n2?CX?F(x)NO?Y,KCF(X)l!U(0,1).u“O?VIIC?C?C?yyy.?Y=F(X)?FY(y),KFY(y)=P(Y y)=P(F(X)y)=0,y 0,P(X F1(y),0 y 1,1,y 1=0,y 0,F(F1(y),0 y 1,1,y 1=0,y 0,y,0 y 1,1,y 1.=Yl!U(0,1).?u“O?VIIC?C?C?)?5P1?YCL!X,3?k?.X|O?
6、)15?p.?0,0,=1y(1+(lny)2),y 0,0,.?u“O?VIIC?C?C?n4?555CCC555?CXl?N(,2),K?a,0,CY=aX+b l?N(a+b,a22).AO/,-a=1,b=,k5eX N(,2),KX N(0,1).u“O?VIIC?C?C?n4?555CCC555?CXl?N(,2),K?a,0,CY=aX+b l?N(a+b,a22).AO/,-a=1,b=,k5eX N(,2),KX N(0,1).u“O?VIIC?C?C?n6?CXlGammaGa(,),c 0,KCcXlGammaGa?,c?.7?CXl?N(0,2),KX2lGammaGa
7、 12,122!.yyy.w,X/N(0,1).uX2/2 2(1),=X22 Ga 12,12!.?X2=2X22 Ga 12,122!.?u“O?VIIC?C?C?8?:X=(X1,Xn)?,Z=g(X1,Xn)?,gRn?R?.X-n=2?/.u“O?VIIC?C?C?8?:X=(X1,Xn)?,Z=g(X1,Xn)?,gRn?R?.X-n=2?/.u“O?VIIC?C?C?n8?C(X,Y)k?pij,i,j=1,2,.(l/)Vp(x,y)(Y/),KCZ=g(X,Y)?FZ(z)=P(X,Y)Dz)=X(i,j):(xi,yj)Dzpij,l/,Dzp(x,y)dxdy,Y/.Dz
8、=(x,y):g(x,y)z.?g(x,y)=x,=?CX?S.u“O?VIIC?C?C?n8?C(X,Y)k?pij,i,j=1,2,.(l/)Vp(x,y)(Y/),KCZ=g(X,Y)?FZ(z)=P(X,Y)Dz)=X(i,j):(xi,yj)Dzpij,l/,Dzp(x,y)dxdy,Y/.Dz=(x,y):g(x,y)z.?g(x,y)=x,=?CX?S.u“O?VIIC?C?C?5?C(X,Y)?XY0101/101/513/102/5.CX?FX(x).u“O?VIIC?C?C?):X?FX(x)=P(X x)=P(X,Y)(,x R)=X(i,j):(xi,yj)(,xRpi
9、j=0,x 0,110+15,0 x 1,110+15+310+25,x 1=0,x 0,310,0 x 1,1,x 1.u“O?VIIC?C?C?e(X,Y)?l.C,KCZ=g(X,Y)l.C,?x.k?Z=g(X,Y)kU?zk,k=1,2,.,?XzVP(Z=zk)=.9e?l.C(X,Y)k?pij,i,j=1,2,.,CZ=g(X,Y)kU?zk,k=1,2,.,KZ?P(Z=zk)=P(i,j):g(xi,yj)=zkpij.u“O?VIIC?C?C?6e?l.C(X,Y)k?Xe:XY01201/21/81/411/161/160CZ=2X Y?.u“O?VIIC?C?C?):
10、kZU?u2,1,0,1,2.u,P(Z=2)=P(X=0,Y=2)=14,P(Z=1)=P(X=0,Y=1)=18,P(Z=1)=P(X=1,Y=1)=116,P(Z=2)=P(X=1,Y=0)=116,?d?K5P(Z=0)=1 1418116116=12.?LXe:Z21012P1/41/81/21/161/16u“O?VIIC?C?C?7?CXYp,X,YO?U/?01.CZ=max(X,Y)?.u“O?VIIC?C?C?):dK,XY,P(X=0)=P(X=1)=1/2.Z?U?k01,P(Z=0)=P(max(X,Y)=0)=P(X=0,Y=0)=P(X=0)P(Y=0)=1212
11、=14,P(Z=1)=1 P(Z=0)=1 14=34.?Z?Z01P1/43/4.u“O?VIIC?C?C?):dK,XY,P(X=0)=P(X=1)=1/2.Z?U?k01,P(Z=0)=P(max(X,Y)=0)=P(X=0,Y=0)=P(X=0)P(Y=0)=1212=14,P(Z=1)=1 P(Z=0)=1 14=34.?Z?Z01P1/43/4.u“O?VIIC?C?C?(l/)n10?C(X,Y)?pij=P(X=xi,Y=yj),i,j=1,2,.,KCZ=X+Y?P(Z=zk)=PiP(X=xi,Y=zk xi)=PjP(X=zk yj,Y=yj)zk,k=1,2,.Z?U?
12、8.AO/,eXYp,KCZ=X+Y?P(Z=zk)=PiP(X=xi)P(Y=zk xi)=PjP(X=zk yj)P(Y=yj).u“O?VIIC?C?C?(l/)n10?C(X,Y)?pij=P(X=xi,Y=yj),i,j=1,2,.,KCZ=X+Y?P(Z=zk)=PiP(X=xi,Y=zk xi)=PjP(X=zk yj,Y=yj)zk,k=1,2,.Z?U?8.AO/,eXYp,KCZ=X+Y?P(Z=zk)=PiP(X=xi)P(Y=zk xi)=PjP(X=zk yj)P(Y=yj).u“O?VIIC?C?C?yyy.UX?,?m?=PiX=xi,?dZ=zk=XiZ=zk,
13、X=xi=XiX=xi,Y=zk xiV?5=?P(Z=zk)=XiP(X=xi,Y=zk xi).e?n?.?u“O?VIIC?C?C?51e,aV?C?Eda,Kdak555.n11?555eCXl?b(n,p),CYl?b(m,p),p,KCZ=X+Y l?b(n+m,p).u“O?VIIC?C?C?51e,aV?C?Eda,Kdak555.n11?555eCXl?b(n,p),CYl?b(m,p),p,KCZ=X+Y l?b(n+m,p).u“O?VIIC?C?C?y:CZ=X+Y?U?k0,1,.,n+m.d,P(Z=k)=XiP(X=i)P(Y=k i)=XiCinpi(1 p)n
14、iCkimpki(1 p)m(ki)=pk(1 p)n+mkXiCinCkim=Ckn+mpk(1 p)n+mk,k=0,1,.,n+m.5P2?p?:?.u“O?VIIC?C?C?y:CZ=X+Y?U?k0,1,.,n+m.d,P(Z=k)=XiP(X=i)P(Y=k i)=XiCinpi(1 p)niCkimpki(1 p)m(ki)=pk(1 p)n+mkXiCinCkim=Ckn+mpk(1 p)n+mk,k=0,1,.,n+m.5P2?p?:?.u“O?VIIC?C?C?n12eCXltP(1),CYltP(2),p,KCZ=X+YltP(1+2).u“O?VIIC?C?C?y:CZ
15、=X+Y?U?k0,1,2,.P(Z=k)=XiP(X=i)P(Y=k i)=kXi=0i1i!e1ki2(k i)!e2=(1+2)kk!e(1+2)kXi=0Cik 11+2!i 1 11+2!ki=(1+2)kk!e(1+2),k=0,1,.?|?b k,11+2!?K5.u“O?VIIC?C?C?y:CZ=X+Y?U?k0,1,2,.P(Z=k)=XiP(X=i)P(Y=k i)=kXi=0i1i!e1ki2(k i)!e2=(1+2)kk!e(1+2)kXi=0Cik 11+2!i 1 11+2!ki=(1+2)kk!e(1+2),k=0,1,.?|?b k,11+2!?K5.u“O
16、?VIIC?C?C?n13?C(X,Y)?Vp(x,y),K?t R,CZ=tX+Y?VpZ(z)=Zp(x,z tx)dx.u“O?VIIC?C?C?y:?CZ=tX+Y?FZ(z),-Dz=(x,y):tx+y z=(x,y):x ,y ztx.uFZ(z)=P(Z z)=P(tX+Y z)=P(X,Y)Dz)=Dzp(x,y)dxdy=ZdxZztxp(x,y)dy=ZdxZzp(x,u tx)du=Zz Zp(x,u tx)dx!du,u“O?VIIC?C?C?uZ=tX+Y?VpZ(z)=dFZ(z)dz=ddzZz Zp(x,u tx)dx!du#=Zp(x,z tx)dx.u“O?VIIC?C?C?n14?C(X,Y)?Vp(x,y),K?t R,CZ=X+tY?VpZ(z)=Zp(z ty,y)dy.u“O?VIIC?C?C?(Y/)15?C(X,Y)?Vp(x,y),KCZ=X+Y?VpZ(z)=Zp(x,z x)dx=Zp(z y,y)dy.eXYp,VOpX(x)pY(y),KCZ=X+Y?VpZ(z)=ZpX(x)pY(z x)dx=ZpX(z y)pY(y)d
