工作文件概率知识点

一、事件的关系与运 AB：AB一定发生，AABABBA，ABAB：AB至少一个发生，ABAB：AB都（/同时）AB：A发生，B不发 ASA：A的对立事AB：A、B 1、P(A)0,P(S)1

SAP(3、性 1）P()

P(A)1P(差事 AB，则P(BA)P(B)P(A),P(B)P(

P(AB)P(A)P(B)P(P(ABC)P(A)P(B)P(C)P(AB)P(AC)P(BC)P(P(AB)P(

P(BA)P(P(

乘法原

P(A)0,P(AB)P(BA)P(P(B)0,P(AB)P(AP(AB)0,P(ABC)

AB)P(BA)P(

ABAPA)PAB)全概率公

A1A2...AnS（S的一个划分P(B)P(BA1)P(A1)P(BA2)P(A2)...P(BAn)P(An贝叶斯公

P(

P(AiB)P(BAiP(BAi)P(AiP(BA1)P(A1)P(BA2)P(A2)...P(BAn)P(An四、独立 A、B相互独立，则P(AB)P(

nApnAk

P(k)Ckpk(1

,k0,1,2,...,

Xn次试验中AXX~B(n, F(x)P(X

F()

F()

F(X)P(aXb)F(b)FP(Xxk) k1,

p

p

p...

k1

F(x)P(Xx)＝P(Xxk)xk xkE(X)x E(g(X))g(x)

k1k k

D(X)(xE(X))2 k

P(Xxi,Yyj) pij

pij

P(Xx)

P(Xx,Yy)

p

i1

P(Yy)P(Xx,Yy)p

独立 X、Y相互独立：pijP(Xxi,Yyj)P(Xxi)P(Yyj)pi三大分

X~

P(X0)1 P(X0) E(X)pD(X)p(1X~B(n,

P(Xk)Ckpk(1p)nk(k0,1,...,

E(X) D(X)np(1

X~

P(Xk)

nkn

(k0,1,

E(X)

D(X)f(x)

F(xPXxf

性 f xbxP(aXb)P(aXb)P(aXb)P(aXb)F(b)F(a)

f

E(X)xf E(g(X))g(x)f D(X)(xE(X))2f(x)dxx2f(x)dx(x2f(x)dx)2E(X2)(E 二维分布函数F(x,y)P(Xx,Yy)f(u,v)du 性质

f(x,y)dxdy

f(x,y)

P((X,Y)D)Df(x,

fX(x)f(x, fY(y)

f(x,

F(x,y)P(Xx,Yy)P(Xx)P(Yy)FX(x)FY

f(x,y)

fX(x)fY(, ,

ax

X~U(a,

f(x)b

E(X)

D(X)ex x

X~

f(x)22

(x

E(X)

D(X)

X~N(,2

f(x)

e2

(x

E(X)

D(X)xx

X~N

(x)

e2(x

E(X)

D(X)

(x)

(x)1()

1e2dx1

e2dx

ex2dx

X~N(,2

xx0aXb~N(ab,a22X*X~NF(x)P(Xx)(x),

P(aXb)(b)(a X,YX~N(,2)Y~N(, XY~N(,22 aXbY~N(ab,a22b22

E(C) E(cX)cE(X

E(XY)E(X)E(YX,YEXY)EX)E(Y

D(X)E(X2)(E(X

性 D(C)

D(cX)c2E(X

D(XC)D(X

D(XY)D(X)D(Y)2cov(x,

X,YDXYDXD(Y十二、协方 cov(X,Y)E(XY)E(X)E(Y

D(aXbY)a2D(X)b2D(YX,YcovX,Y)X~B(n,p)(n大

XE(X)

D(XnpD(Xnp(1

~N

P132Xnp(1np(1Xnp(1np(1

}

x np(1Xnp(1np(1Xnp(1

xnp(1xnp(1xnp(1

x P(aXb)

X

bbnp(1

}

b

np(1)np(1

a aanp(1np(1np(1

X1

E(X)E(X

D(X)D(X

E(S2)D(XS1 (S1 (XX2n

S21

(XX

S n

上

P(Xx)

[F(x1PXx)]z1 t1XYniiX~NXYnii

X2~2

E(2(n)) D(2(n))X~N(0,1Y~2(n)

X~2(n),Y~2(n)

F(n,nXY XY十五、抽样分布定 如果X~N(,2 X,X,...,X为其一个样本（容量为n， Xn