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1-3 23 , 1/4.: x,y, (x,y), :xyO111/4xy=1/4

:

, , . , . , , , . .

2.1

, ,, , .

1. , ., , , 1,2,3,4,5,6.

2. , , ., , ""1, ""-1, , ;

, , , , .

, 1 S, SX=X(e).: .Se1e2e3X(e1)X(e3)X(e2)OR

Xe. , XaS, A={e|X(e)=a}S., A{X=a}, , A={e|X(e)=a} {X=a}

X,Y,Zx,h. , x,y,z.:, , ., .

1 , , 1, S={, }, X, XS

2 , H, T, S={HHH,HHT,HTH,THH,HTT,THT,TTH,TTT};HX, XS

eHHHHHTHTHTHHHTTTHTTTHTTTX32221110

, X2A={HHT,HTH,THH}P{X=2}=P(A)=3/8,, P{X1}=P{HTT,THT,TTH,TTT}=4/8.

eHHHHHTHTHTHHHTTTHTTTHTTTX32221110

3 , [0,+), X(), XS={t|t0}, X=X(t)=t, .

, , ., 120X.{20}{X20}, {10}{X=10}.

, . . , .

2.2

, X, , X.x1,x2,X, xi, {X=xi}S, X, ().

1 Xxi(i=1,2,),P{X=xi}=pi, i=1,2,X, .X:

Xx1x2xnpip1p2pn

, pi,(i=1,2,):

Xx1x2xnpip1p2pn

1 0.9, X. X0,1,2,P{X=0}=(0.1)(0.1)=0.01P{X=1}=2(0.9)(0.1)=0.18P{X=2}=(0.9)(0.9)=0.81P{X=0}+P{X=1}+P{X=2}=1,, X

X012pi0.010.180.81

2 X:a. a=e-l

:XX, ,

Xx1x2xnpip1p2pn

, X1:P{X0}=P{X=0}=0.01,P{X

, 1. 2 X1, P{X=a}=1,Xa.: , , , .

2. 3 X, P{X=x1}=p, P{X=x2}=1-p, (0

, A, 0

3. n4 Xn, , P{X=xi}=1/n, i=1,2,,n,Xn{x1,x2,,xn}.: n, , S={e1,e2, , en}, X(ei)=i, P{X=i}=1/n, i=1,2,,n, Xn.

4. n, Ap, XnA, X0,1,,n, k(0kn), {X=k}"nAk", , (2.2)

5 X(2.2), Xn,p. X~b(n,p)(B(n,p)).(2.2): n=1, (2.2)P{X=k}=pkq1-k, k=0,1;q=1-p, X0-1.

nOpkn=10, p=0.7

nOpkn=13, p=0.5

, np, k, P{X=k}, . , . (1) (n+1)p, P{X=k}k=[(n+1)p];(2) (n+1)p, P{X=k}k=(n+1)pk=(n+1)p-1.: [x]x.

3 1005, 3, 1, 32. 3, 3, . , 0.05. X3, X~b(3,0.05), , :

2-2 521,2,7,10