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1、第二章習(xí)題部分解答1.解：由矩估計(jì)法：8??1?a=X=74.002=∑xi?8i=1?821?σ?=S2=×610?6=www.khdaw.com∑(x?74.002)2i??8i=1?2n28?6?6∴S=S=××610=6.85710×n?181?課后答案網(wǎng)2（1）解：由矩估計(jì)法：α=A=ξ11'θ2(θ?x)θα=EX=xdx==ξ1∫20θ3∴=θ?3ξwww.khdaw.comα=A=ξ11（2）'1θθ+1α=EX=x(θ+1)xdx==ξ1∫0θ+2?2ξ課后答案網(wǎng)?1∴=θ1?ξ（3）x?θ
2、1?+∞1θα=e2?xdx=θ+θ=ξ1∫12θ1θ2x?θ1?n+∞1θ1α=∫e2?xdx2=A=∑X2=θ2+2θξ22i12θ1θ2ni=12www.khdaw.com2?2∴A=S+ξ=θ=(ξθ?)+2θξ222??θ=?ξS1∴???θ=S2課后答案網(wǎng)N1NN(+1)1（4）A1=ξ=∑xi=?i=1N2N?N?=2ξ?1（5）1θ?1θA=ξ=xθxdx=1∫0θ+1?ξ2www.khdaw.com?θ=()ξ?1∞2k?22（6）A=ξ=∑kki(?1)θ(1?θ)=1k=2θ2課后答案網(wǎng)
3、?θ?=ξ3.解:設(shè)A={ξ<0},X表示A出現(xiàn)的次數(shù)，2(xa?)01?PA()=P{ξ<0}=∫e2dx?∞2πξ?a0?awww.khdaw.com=P{<}=Φ?(a)=p≈0.7,11∴p≈0.7,a=?0.525課后答案網(wǎng)4.解：nθ?(θ+1)(1)()Lθ=∏θcxii=1nln()Lθ=∑[lnθθ+lnc?(θ+1)ln]xii=1nn?ln()Lθ1θ=∑[+lnc?ln]www.khdaw.comxi=+nlnc?∑lnxi=0?θi=1θni=1?nθ=n∑lnxi?nlnci=1課
4、后答案網(wǎng)nθ?1(2)()Lθ=∏θxii=1nln()Lθ=∑[lnθ+(θ?1)ln]xii=1n?ln()Lθ111=∑[+ln]0xi=?θi=1θ2θ2θ2?nwww.khdaw.comθ=n2(∑ln)xii=1課后答案網(wǎng)n11(3)()Lθ=∏=ni=1θθln()Lθ=?nlnθ?ln()Lθn=?=0?θθ?1?1?,,ξ…,ξ≤θ?,ξ≤θn1nn()n∵L()θ=?θwww.khdaw.com=?θ??0,other??0,other11≤,()Lθ≤L(ξ)nn()nθξ()n課后答案
5、網(wǎng)θ?=ξ()nn(4)()Lθ=∏Cxiθxi(1?θ)Nx?iNi=1nxiln()Lθ=∑[lnCN+xilnθ+(N?xi)ln(1?θ)]i=1nn∑xi∑(N?xi)?ln()Lθi=1i=1=?www.khdaw.com=0?θθ1?θ?xθ=N課后答案網(wǎng)n121?2(xi?θ)(5)()Lθ=∏e2θi=1θ2πn2(x?θ)iln()Lθ=∑[ln2πθ?]2i=12θn22?ln()Lθ?2πn?2(x?θθ)?2(x?θθ)ii=∑[=04?θ2πθi=1www.khdaw.com2θ2
6、n?ξ12ξθ=+∑ξi?4ni=12課后答案網(wǎng)nc?(c+1)(6)()Lθ=∏cθxii=1nln()Lθ=∑[lncc?lnθ?(c+1)ln]xii=1?ln()Lθnc?=?=0不能解出θ，所以由?θθnwww.khdaw.com?c?(c+1)L()θ=∏cθxi,θ≤ξ1,…,ξni=1L()θ≤L(ξ)?θ?=ξ(1)(1)課后答案網(wǎng)n2xi?2(7)()Lθ=∏（xi?1)θ(1?θ)i=1nln()Lθ=∑[2lnθ+(xi?2)ln(1?θ)ln(+xi?1)]i=1n∑xi?2n?ln
7、()Lθ2n2i=1?=?]0=?θ=?θθ1?θξwww.khdaw.comn(8)()Lθ=∏θδ()xi(2)θδ(xi?1)(13)?θδ(xi?2)=θn0(2)(13)θn1?θn2i=1?ln()Lθ?2?ξ=?0θ=?θ課后答案網(wǎng)45.解：∵ξ~U(,0)θn11(1)()Lθ=∏?=n,θ<ξ1,…,ξn<0i=1θ(?θ)θ?max=ξ,()Lθ≤L()θ?(1)∵ξ~U(,2)θθwww.khdaw.comn11(2)()Lθ=∏=n,θ<ξ1,…,ξn<2θi=1θθξξξθ?=()n
8、,()Lθ≤L(),θ?1,…,n<θmin2課后答案網(wǎng)22nn6.解：1?x?θ(1)()Lθ=∏fx(,)θ=∏eiii=1i=12x,…,xx
9、xi?θ
10、1∑x()k?∑x()l+(n?2)iθL()θ=ei=1=ek=1li=+1nn22?ξ,n為奇www.khdaw.comn+1()?2??θ=?ξ+ξ時(shí)L()θ達(dá)到最大值
