1

.,.X ~N ( , 2), , 2, , .

.

1

, , . .

X, , X.

1 , X, l>0, l, , l.

X~p(l), l=E(X). E(X). E(X)=l1.22.

: XF(x;q), q. X1,X2,...,XnX, x1,x2,...,xn.

:

() X, f(x;q1,q2,...,qk), X, P{X=x}=p(x;q1,q2,...,qk), q1,q2,...,qk, X1,X2,...,XnX. Xk(RXx), , q1,q2,...,qk.

ml(l=1,2,...,k), . . .

:kq1,q2,...,qk. q1,q2,...,qk,

Aimi, i=1,2,...,k, qi, i=1,2,...,k, . .

2 X~U(a,b), a,b. X1,X2,...,XnX, a,b.: m1=E(X)=(a+b)/2 m2=E(X2)=D(X)+[E(X)]2 =(b-a)2/12+(a+b)2/4.

A1,A2m1,m2, a,b:

3 Xms2, s2>0, m,s2. X1,X2,...,XnX. m,s2.A1,A2m1,m2, ms2

() X, P{X=x}=p(x;q), qQ, q, Qq. X1,X2,...,XnX, X1,X2,...,Xnx1,x2,...,xn. P{X1=x1,X2=x2,...,Xn=xn}

q, q, L(q)(, x1,x2,...,xn, ).: x1,x2,...,xn, L(q) . x1,x2,...,xnqQq. q=q0QL(q)QL(q), q0q.

, x1,x2,,xn, L(x1,x2,,xn;)

, ,

x1,x2,,xn,

,.

.

_1113407958.unknown

_1113408121.unknown

_1113408376.unknown

_1113407974.unknown

_1113407902.unknown

X, f(x;q),qQ, q, Qq. X1,X2,...,XnX, x1,x2,...,xn, (X1,X2,...,Xn)(x1,x2,...,xn)(dx1,dx2,...,dxnn)

. ,

(1.3),

. L().

,

.

_1113417244.unknown

_1113417526.unknown

_1113417640.unknown

_1113417698.unknown

_1113417397.unknown

_1113417170.unknown

, p(x;q)f(x;q)q, q. L(q)ln L(q)q, , qq, , (1.6).

4 X~b(1,p), X1,X2,...,XnX, p.

x1,x2,...,xnX1,X2,...,Xn. X P{X=x}=px(1-p)1-x, x=0,1.

q1,q2,...,qk. , L. k, qi (i=1,2,...,k) . (1.7) .

5 X~N(m,s2), m, s2, x1,x2,...,xnX. m, s2.

X

6 X(a,b), a,b, x1,x2,...,xn. a,b. x(1)=min(x1,x2,...,xn), x(n)=max(x1,x2,...,xn). Xax1,x2,...,xnbax(1),x(n)b.

ax(1), bx(n)a,bL(a,b)a=x(1), b=x(n)(x(n)-x(1))-1. a,ba,b

: u=u(), ((=(u), u(U,

X,

u().

,

,

x1,x2,,xnX,

_1113547620.unknown

_1113548003.unknown

_1145686617.unknown

_1145686752.unknown

_1113547884.unknown

_1113547546.unknown

. , 5s2s

2 ()

, T. T, . , , .

, nt=0, , . , (0 t1 t2 ...tn). , , .

: . nt=0, t0. m, 0t1t2...tmt0,m, t1,t2,...,tm.

. nt=0, m(m, m

,q >0. n,m, 0t1t2...tm, q(). [0,tm]m,n-mtm, n-mtm.

q, . [ti,ti+dti]

dt1,...,dtm. q,

qs(tm)=t1+t2+...+tm+(n-m)tm, tmn

0t1t2...tmt0(t0), , q s(t0)=t1+t2+...+tm+(n-m)t0, t0n.

, q >0. 50, 15, ()115,119,131,138,142,147,148,155,158,159,163,166,167,170,172.

n=50, m=15, s(t15)=115+119+...+172+(50-15)172=8270, q

3

1

X1,X2,,XnX. (X, .

, (

(3.1)

.

_1113657581.unknown

_1113657659.unknown

_1113657716.unknown

_1113657536.unknown

. .

, X, 2>0,

,

2.

S22.

_1113658073.unknown

_1113658320.unknown

_1113658376.unknown

_1113658242.unknown

_1113658028.unknown

1 Xkk=E(Xk)(k(0), X1,X2,,XnX, , k

kk.

X1,X2,,XnX,

(3.2)

_1113659004.unknown

_1113659072.unknown

_1113658863.unknown

2 X,

. Z=min(X1,X2,...,Xn)

q , qQ, qQ,

3(2) n>1, q D(X)=q 2,

() , q: e>0,

2081,2(4),410