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0.5

){|

|0.10.1}{}0.50.5

0.10.5

2.97n2.N,(a,

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0.140(2)[|

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4a,tn

4N)n[|t2

0

t

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dt

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n

800

255(3)P{|t|P{

|t0.10.1}()4n

n2

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~4(12,5135{13}P{})0.130.82{{{

,

P{5{10}]5110{1}]25

P{

(5)

{

(5)

15}{15,215P{

15}}]5

5.

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0.0015exdx]6800{

P{3000}]6

3000

0.00150.0015dx]6(166.

0

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mi

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,}n,i

)pqk)n(nni

itit12212kkk7．itit12212kkk

(

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it())]nnn

itit)itit2n2n

n

8.

3~(20,~(20,)10151~N)12|P{|0.3}{}()0.67均值的和（差）等于和的均值，方差的和差都等于方差的和9.

E((由中心極限定理：i

in

(0,1)

ii

(0,1)

ii~(n

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),D))22(kkkaEDA)2kn

2

kAk

(a,k

a2k)n11.

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n

nni123(02nni123(023(x)28226113.

,,(ii

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nD2Dn

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n(ni

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2

14.

ns2(ns2E()n

2

n()n2(n2D()2(nDs()n2n15.

1)123

(1)D

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(

'

A

'

2

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11111

BEBB'

5

1

(B

'

(11)2016.

1(21

1221

1＝2‘151＝2‘153001112111b22

1，1，則110231

分布為(A),22

1

1118.

1＝=A1123N(),

0111時(shí)獨(dú).1221.

N

I)n(B(Atr(B)(AB)((tr()

A(

AE

B

trA)()

tr(AB)

tr(

tr(B)

trAB)22.

y112

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28

2

a12

747

ijiin1F(xijiin1F(x23.

n,),N

),ns2

~

nn

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/(t(24.

,,),,,n)'111),Dn1iiii又DD2,0,

n則令則

nN(n()iiinii

2i

)I)n(

n

與

獨(dú)立，則

獨(dú)立，且

~(n26.

1(,)2x則f(x220otherf()()[1(x

12f

()

()(x)[()]

12f(xy)(f(x)f(yF()()]]

1nni27.1nni

Yi

N

),(d)

ni

Y

12

e

y2

dy

2D()()2()

n2

i

2i)2

33.

2(1)nn2),N(0,)ii

(9)i10P{i}0.3{i

i0.3

)

2}0.01(2)0.3109t(9)s

ns2

({{0.99}snsn(3)NN2122N(0,1)0.180.1812)(1),(1)0.18{(12)0.9

(1)4

13{

41

2

P{

4(13)0.12

2

}0.950.12

nnnn34.nnnn

(1)

i

(0,

n

i

(0,m

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ii(i

)

2

i(n1),(i)m

2

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i

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n

i

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ii

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i

i

Nn

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nii

n),

ii

)i)2nii/mi

Fnm

n《應(yīng)用數(shù)理統(tǒng)計(jì)》參答案

iiS2x(2221.由矩估計(jì)法iiS2x(222

2

xi82(74.002)i

22n8

2.

由矩估計(jì)法EX

'

)3(2)

EX

'

A1

2(3)

1

2

122

eX2i

2i1A22(4)

A1

i

1N(Nx2N(5)

NA)

(6)

A(k2

2

nniininninni,,,1(nnnLnniininninni,,,1(nnnLother0,otherother0,other()()3.

設(shè)X表出現(xiàn)的次數(shù)，(A){

0

2

xe{

}p0.7,4.

L(

xi

ilnLi

cx]i[cln]lnlnxniilnxlnciii

ln(i

]in11[]2i

nxi

2i(3)L1(3)LilnL(lnL(L(nL(1,,,L(1(n)1L)nL((n)()(n)L(i(1iL

i

i

ii

1iinnnninn1iinnnninnL(i

(2

lnLi

(xi2

]Lnx[ii2i14i

(6)Li

i

clnL(ln

1)lnx]iiL不能解由Li

,

1

,

niLL()

ii

(1

xlnLiLn

x2)ln(1xiini2i]5.

U((1)L

ni

,(

1

,

n,L

n)1niii()(1nnni0nnin)1niii()(1nnni0nni~UL

ni

1

1

,

,1

nL(1,2226.

(fi2iix,,xxn(1)i(i

(n)1Liel2n2n

xi)(l)

,為奇(,n2

時(shí)L(到大值7.

1,2L(

ni

())

(1)

)

or

所以不唯一。8.

(1)L(

),ln(

i0

i

iL(i

xnti

x

0iLt))L()[ln0

x)i0

L()

it1

i求不出結(jié)果ntL()(t)()i,tt0(1)0(1)

9.

i1nii1niL(

)

i

1

e

(xi

1

e

i

xilnL)lnL)

i

xii

nL)nn2

10.~(a,),N(a,),(0,n

nn

),1n1nE|kii

1nn

2

i

(

1nn

k

2n11.Ni

),|

i

x

1

x2

dx

x

12

x

dx

2

2

12.

1n2EE|nni1(/D(nI(

12312nnnn12nn11112312nnnn12nn111E,(ii3Eaa,E510EaEE,39131982DaDD105DaD,都是無偏估計(jì)量小213.

EaEaD)D)112

cov()Da(a)2

Da

Daca)1222

L(Dc,c)2c12212cc1

c122

,c113.

,(1)N(a,5),(a)11

i

2

e

(x)i

lnL(i

(xi2

2

]L(a)nx)iiii0,iini(2)N(a,),(),14n,(1)122414D'(n)n(n)2n21(3n)(n]

nnnn12nn111111(2211(),1i1in12n12(1)12112111111[dx1111nnnn12nn111111(2211(),1i1in12n12(1)12112111111[dx1111111DXnx[dx)(1)()14.

a(a,5),L(a12

i

125

e

(i

L(a)10i

(x)i210

2

]15.

L()2()iiiiiini14N(a(a,nn1214(nn)1214'D'(n)2n2)21n(3)(n]),E2222DDi(1)g(x)nf()[1(x)][g(x)nf()[1(x)][11[2n2nDX2[dx)2n22的密度函數(shù)為()()nf(F(x)]n[xn

1nx[x2

nx[

11)2

(1)(n)

[E]2

(1)(n)

[DD](1)()

(1)

()

較有效

11122iiiinnii11122iiiinnii17.

E(D；1212又()1122122D(c112

)2D2D()2122c2)DcD)122112令()c1112則f'(c)cc318.

(EX11

2DX

ni

2i21.22.

211nniineL!(2)iilnLiiEL(f(x,ii=1i=1lnLlnii

)1(L(i

lnx

i

lnxiL(1（）ln[i

i

lnxi

)]()(

i

lnxi

)

()

i

lnxi

nnnnin00inn015inS(,),0.95（）T,則(T)=0,即00nnnnin00inn015inS(,),0.95dx0ini等式左右兩邊關(guān)于得

[n0

xii

iii

lnx]i1

dxn

(0

nnnlnx)ii

xi1

dxn即)E(lnx)]ilni1i[(i)]()n23.a的區(qū)為(),n

ii0.58,tn151()(1.67nnni求區(qū)(0.0848,1.2448)(nn121

ii)(n

0.766,

ii)(n

為(24.

a

210

*

i

xi52，t((9)n91

S*t

(5.778n10

0.607

S

*t1

(n

5.77810

3.393區(qū)間為

1022152nS21123a(uv)e21022152nS21123a(uv)e20.95的區(qū)間為(

2(22

nS2(

nS2

i10(i)(9)

i10(i)15.639(9)求區(qū)間25.

f(x

x|y)

e

i

xi

y

e

xy

h(|,

x))(x,1

|)y

yexy

x)

n

1

)當(dāng)X

,

n則(

n126.

1(x)N(1

1

2

(

)2

)

(,a)[L(a)]E[3aa

2

23(a)]55

2313a2((a(a5

2

())2

d1u1v2

23552

u

2

即1即1同理

1325a2(,a),Ra,a),66最小。27.

d(

L()

2

0211

3

20a1aa1L)1a

又

(

1a0又P((11P(P(,22PP(d)E[L()]11a)()L()(1123(,)E[()]22(a)(L(,a)PL)P2121144(d)E[Ld)]31(,a)()PL)313230,

0()2

3080000（2）

L(d23

d

101

101

101P(P(0,1P(PP(,4P(0,Pd)

0,2（3）

L(d

d

1

1

223

011933.

P(P(0,1P(PP(,4P(0,P)1d為最大風(fēng)險(xiǎn)最估計(jì)量1L)

0600001(d)[]30002(d)E[]0.950.3(d)E[]80003dimax決策。）R[]0.751500[,d]0.758000應(yīng)買

）)((x(P(x)0.750.950.250.30.7875()E[）)((x(P(x)0.750.950.250.30.7875()E[d|x]La)()L()P|x11111210.750.25571.2,0.750.95()E[d|x]La)(x)L(,)(|x)0.250.2125()E[)x](1L)()L,)(xx)571.2*0.78751412*0.2125(((d)1500750500應(yīng)請(qǐng)np37.

）)(P()111110.750.950.250.30.7875'()E[(dx]11La1P2a(x10.750.25571.2,0.750.95'()E[(dx]LaP(xL2aP(x12122220.250.2125()E[(d)]1La)P)L,)(xx)571.2*0.78751412*0.2125112112(d)1500750500應(yīng)請(qǐng)B(10,p)(1)EXx

L(p,

xxii

xi(1)10L(p)

ilnp)ln(1p)]iiiii

ii

ii

(xp)(1p)pLn(x)(1p)又，所以效估量(p)

np(1

,R界為

1p(1p)，I(nInp

()n(p)p所以p為p的有效估計(jì)量，2pp2

n）hy|x,n

,)f(1

,xy)f(x

,x|)Cii(1)10i

,

x

)nx為參數(shù)nx10n貝塔分布的.|(nx1,10所以(|

nx(nxnn《應(yīng)用數(shù)理統(tǒng)計(jì)》參答案1．

B1，pi

B(10,i(|iiii(1|p0.2)ii0.20.830.20.8740.2[0.624190.03299]0.408

0.8

pii0.5230.50.540.50.989260.623050.3662

0.5

2.

(a(

1.5)(1.5)0.93370.066819(xa(

)1.5)(1.5)3.

H：500,H:1,

x(為拒絕域sn而

，所以機(jī)器工作正.4.

222H：:1222

1000U

|2.51.962

拒絕H，即認(rèn)為元件不合.05.

:x0.5099,

x10.20.5099n201.7291，值顯7.

H：0.04%,H:

2(0.037%)2

8.5561

(n=16.9198.

所以不否定即認(rèn)為0H：0.005,:0.005

ns2

(0.005)

(=15.5079.

所以拒絕即為導(dǎo)線不合.0:212與

12

nnor

12

<F1

n10.

n2n(122(59,39)1.74F.0H：H:1212S12Sn(n271=1=Sn(812

=0.5611.

F(7,6)F(7,6)所以接受H兩產(chǎn)品精度無顯著差0

5mHa,H:a01225m=未n121T

S212

1

(為拒絕域又

2

0.93962.2622，0.975接受H,即量無顯著差012.

1

1.2

2.1247.91.22

n=27.48813.

即劣0H：a,H:a0121=知12

x

n

9

0.975

(9)2.2622，14.

接受H,即認(rèn)前后均無顯著.0H：(),H:F(x)F(xF(x)為泊松分布0010ivi估計(jì)值inpi

2i

ppi0

,ppe10

,n

i

inp

7v2inpiii15.

<m12.5921-0.95接受H即認(rèn)為分布為泊松分布.0(),HF(xFx),F(為泊松分布0i,估計(jì)為i0.805i

i

i

0.805

pe

0.805

n

i

v2iippii

i

(1-0.95能認(rèn)為分布為泊松布016.

np010(),:(x)F(x),P{}010np010

110n

miii

110

5.12517.

<((9)1-,布.0H：F(H:F(x)(),P{X}k10

p.p未估值

x0n100

0.01p010

0.368,p0.368,n

i

v2inp

i

i

v2inp

i

18.

<(m1-接受H,能認(rèn)布二項(xiàng)布0F()(yH:F(x,y)(x)y),r拒絕域?yàn)閧n

i

ni..k

1-

(r1)}n

0.0479

(2)c

和患者14737210健康12322和受H,認(rèn)為慢性氣炎與吸煙量無關(guān).0

ATiijATiij《應(yīng)用數(shù)理統(tǒng)計(jì)》參答案1.

T838,T23xxx