四、随机变量的数字特征(答案)

.概率论与数理统计练习题系班E(X)E(X)是B[[]]Xx1xe019Xf(x)E(x9CX)90x0119xxexxe19992DE)()E[]3E)E)2E)E()2333X,,E(X)1(x1)29Xf(x)(21)EXe28221116/15X012EXX(3)X2P10(x)e(x)()EXXfx||253X3E(X)1136CC2323P(X3)P(X4)P(X5)，34101010CCC3555133E(X)3455实用文档..2(1x)0x1Xf(x)E(X)0其它1E(X)xxdx12(1)30~N(,)EXX21x(x)22y2yedyx||e令||dxy2y22yedy200exxXf(x)0x0eYmax{X,2}2Ymin{X,2}3Y2X11ee0E(Y)2xx32edxxedxY)2Exx20222ee2e222Y)2xedx2edxExx3021e2e1e222概率论与数理统计练习题系班E(X)D(X)3[3(X2)][B]2实用文档..DX~B(n,p)[[]]EX2DX4npp)1DX4np(1p)EX41D3么E)23D)23E)2D)2E)23D)43E)23D)4X,,D(X)12(x)e(x)()DXXfx||2D(X)1/3X[E(X211/22(X)DYe(yX,,Y2X1的E(X)123D(X)E(X)(EX)10.340.590.2(1.9)0.49222EY)2E(X)1DY)4D(X)X~NE|x|D|X|E(X)E(X)、、3与4实用文档..x2e|1x22x2dx2x2=E|X|x|eedx022202D|XE(|X|)(E|x|)E(X)2221x2x2edxxx2x2x2edx=1E(X)de[xe]2222222D|X1x3x2=0(X)eE32x4x2x3x2x2x2=3(X)e3eE42220x23(x)c2x4()2,(1，EXXfPX40C2E(X)aD(X)；YeX2xaxdx4x(bxcdx02bc8x|x|x|ab6c3203422423323383ab6c2得3343得a253PXbc24f(xdx12a6b2c1得实用文档..11,b,ca44141222D(X)(xf(x2x(x4xx40223111xxx22EY)ef(x24xe(e4440212x222DY)EY)(EYef(x[(e]2241x1e2x1x11(e|[(e][(e)]2x202x422242424244211(e)[(e)]4222241e(e2224概率论与数理统计练习题系班X和YE()B[]D()D(X)DY)D(XY)D(X)DY)X与YX与YD(XY)D(X)DY)[A]与YF(x,y)F(x)F(y)XY实用文档..1与YXY(X,Y)NDXY)(X)6DY)3DXY)，X与YD．(X,Y)1001XX与YX与YYX1XP00111Y1XPE(X)().0.1.0EY)().0.1.0E()()().()0.()1.01()00110=0E()E(X)EY)0xyX与YP(X,Y)0.≠P(X)PY)..X与YD(X)25,DY)36,0.4D(XY),D(XY)XY0.45612(,)XYxy()()DXDY，D(XY)D(X)Cov(X,Y)DY)D(XY)D(X)Cov(X,Y)DY)实用文档..~NY~UYE(),D(XY),DXY)X40424E(X)0,D(X)4，EY)2DY)，，023xy,E()04,D(XY)D(X)DY)433DXY)4D(X)9DY)2x0x155e(y5)yy(x)f(y)YYf，0其它0XE()2x323E(X)1x2|1030EY)yedyeey5y(1)|6(y5)552E()E(X)EY)643(Y),E(X)EY),(X),Y),.5W。2XYa使EW)EW)2X2Y(X,Y)D(X),DY)a222XYXVX与随机变量WWaX6Y222EW)E[aX6aXYY]aE(X)6aE(XY)9EY)222222a[D(X)(E(X))]6aE(XY)[DY)(EY))]2224a24a2实用文档..(a6a36)[(a)27]22当a3EW)XVXE)EW)EV)0与WWV)EW)EV)E(XaY)(E(X))a(EY))E222222D(X)aDY)2a0222XY2X2a。2Y概率论与数理统计练习题系班是nApAnnn}0lim{p[A]n010(X)1.1,D(X)0.1E[B]21XXXX},X,,XX~B(1,p)3．X121000i[D]1b1000pa1000p1000paX}()()X10001000pq1000pqiii1i1实用文档..X~B(1000,p)aX}b)(a)iii1i1E(X)D(X)1PX.2．X和Y22和和140.5PX1.Y6kgkgkgiXiiE(X)50000.52500,D(X)50000.0150.iii1i1XiP(XP()i1ii11(1(？1(0.5,0.5),E(X)0,D(X)1500125.XU12iii1i1X15355iP(|X15)P()()](1.34)]0.18.i1125125ii1实用文档..n|X|10nnni(|XP()0.90().Pi1ini11212n()2n443n查1X0.XiiiX,YB(100,0.8),EY)80,DY)16.令Yii1Y755PYP()()41iX0.X令YiiX,YB(100,0.7),EY)70,DY)21.ii1Y755PYP()1()1X11215Xi...P030205实用文档..E(X)1.3.20.21505129(i,2,,300)i(X)1325)(i,,,)2iX记Xii1300129400300129X..P(X400)P3000048930000489