概率论 复习题.pdf

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1、
1AB()A.P(AB)=0B.P(A∪B)=P(A)+P(B)C.P(AB)=P(A)P(B)D.P(B−A)=P(B)2.11ABP(A)=3,P(B)=5,P(A

2、B¯)=A.1B.1C.4D.11551533.20.012
0.80.10.1!"#$%&4'()*.!:(1)'
;

3、(2)"',#$%&
.4.'+10(82-'+1X.)*/+.(1)+,0*-!X12(2)+0*-!P(X=3).5.A,B#"P(A)=0.7,P(AB)=0.5P(A−B)=?6.ξ3.104/5016+/16
0.4ξ22+23E(ξ)=?7.7&50567(208309.8"90*

4、$:-7#7,:;9<87
=;?8.><=#Æ?ξ@ηE(ξη)=EξEηA.Var(ξη)=Var(ξ)·Var(η)B.Var(ξ+η)=Var(ξ)+Var(η)C.ξ>ηD.ξ>η19.X,YAB?CD+Cy(1−x),0≤x≤1,0≤y≤xp(x,y)=0,(@(1)!A+C;(2)X>Y)E10.2ξ#Æ?ξ"BF(1,2)CG-HD1!#Æ?η=e?CD+.11.EIFGKHHIX&1?CD+2,

5、x≥1x3p(x)=0,(@8"JKLIMLNMOGNKH(PN<
QR0.01)OIM;JK=;E(SPIMCQIMRT>HIRT)12.3&#Æ?X@Y,TP(X≥0,Y≥0)=7,P(X≥0)=P(Y≥40)=,P(max{X,Y}≥0)U0)Poisson1,IY"W
p(0)VY3.W9+!Z(1)"[W&nY&m9W
2

6、(2);X#Y?(X,Y)AB1.114.X,YHG-Z1N(0,)#Æ?#Æ?2

7、X−Y

8、+23E

9、X−Y

10、=?15.#Æ?XG-X+λPoisson1TE[(X−1)(X−2)]=1,λ=?16.#Æ?X?CD+1cosx,0≤x≤πp(x)=220,(@π2>X$4%]10[Y3.%^<3+!Y+23E217.E_&N`WW]a-1

11、η)G-;_Z1N(0,0,σ1,σ2,ρ),!ξ+η>ξ−ηcdJE19.-n`a 2r(2r≤n)!
Z(1)%&`a2(2)be&`a20.#Æ?Xn,n=1,2,···f&3@ghcdi)&eghCov(Xi,Xj)<0,{Xn}G-^+jf.21.X1,X2,···1#Æ?gghk"(hYn=Xn+Xn+1+Xn+2,n=1,2,···,cY1,Y2,···G-^+jf.22.EijlmB0.0

12、1Ook'Æ=;ijlpLl(&100B
m<0.95E23."BF(0,1)C#$nT!qnTFqr+23.24.2X∼χn,csn→∞QX−nL√−→N(0,1)2n25.2opqot&ru4_4.5_5_(sot#ruot
0.30.20.5(TE200o[uvvjw!wx"910_930_F
(26.`x#yzW,z25ÆY<9,{IY

13、&}L"

14、W,~@{W>).

15、zW&"&9WQpW,!'zWW++23.27.~~cBernoulli^+jf.28.D+}E#Æ?1D+()3(A)F(x)=1+1(B)F(x)=1+1arctanxx22π1(1−e−x),x>0(C)F(x)=20,x≤0x+∞(D)F(x)=f(t)dt,(f(t)dt=1−∞−∞29.X1,X2,···,Xn,···

16、G-BF(0,θ)CHD1#Æ?g,hYn=max1≤i≤nXi.(