概率论试题十二套

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31©ᓭᜧ«(¬)29.BC®EXḄᑖ#ᑡ-10PlP2P3u)E(X)=0.1,E(X2)=0.9,T(1)D(-2X+1)Z(2)pi$p,P3Z(3)XḄᑖ#²ᦪF(x).2´ஹµᵨ⚪(ᐳ10ᑖ)30.20·¸ὅᑖgº$;º10·.ᙠgºᑁᑖyᵨAஹBg¿ÀÁ$ÂÃᵨÀÄÅḄṑḨÈ$ÉÊA¿ÀÁÅÈḄ᪵/ᙳË\᪵/ÌÍᑖyÎ=2.33,sZ=6.51ZB¿ÀÁÅÈḄ᪵/ᙳË\᪵/ÌÍᑖy3=0.75,s=3.49.ᎷAஹBg¿ÀÁḄÅÈᙳ᝱ᑖ#$gὅÌÍ_Ò.[ÓᔲÔAஹBg¿ÀÁÕÅṑḨÈḄᦔÊ×Ø℉ÍÚe(Ø℉ÛÜa=0.01).(▬to.oo(l8)=2.8784,10.005(20)=2.8453)5ீᔁáுRᔁ(w)ᓫ⚗⌱æ⚪(;:⚪3ᑖ$ᐳ15ᑖ)(A)0;(B)1;(C)0.6;(D)1/62.1ஹ2ஹ3ஹ4ஹ5è´éᦪê&ÒÓëᙢஹᨵíîᙢïðñògéᦪê$ᑣègéᦪêó_lḄᭆ᳛(D)124(A)-;(B)—;(C)—;(D){ôóÕ225253.ᢗögéᙳᒴḄøù$u)úᦪûW]Ꮤᦪ$ᑣúᦪûW6Ḅᭆ᳛(A)511(A)—;(B)w;(0-;(D){ôóÕ18324.wBC®EḄᑖ#²ᦪý஺)=ÿ⁐-,(a=0,b=Dᑣ(0)Ḅ(C)3+e*(A)0.1;(B)0.5;(C)0.25;(D)5.ᨵ3#$ᳫ&2#'ᳫ()*+,-.᥎0ᳫ(᥎1$ᳫ15ᑖ(᥎1'ᳫ12ᑖ(ᑣ3ᡠ1ᑖᦪḄᦪ678(C)(A)2.5;(B)3.5;(03.8;(D):.;<⚪(>?⚪3ᑖ(ᐳ15ᑖ)1.A48CDEFGḄ-.HI,J(K=0.5,ᡝ(ঠ=0.7,ᑣP(AUB)=_0.85_.2.A-.RST~8(஻(p),EY)=3,஺(4)=1.2,ᑣ/?=____.3.-.RS§Ḅ78E(J)=5,᪗`a஺■(4)=2,ᑣE(42)=_____.4.ᵬஹefghgi#j᪗(3kgj᪗Ḅᭆ᳛ᑖnC0.7&0.8.ᐜᵫᵬgi(qᵬrgsᵫegi஺Af*ḄgiCDEFGḄ(ᑣj᪗tgḄᭆ᳛.32

32"v,wᓭᜧ6z{|}5.A~-.RShḄᭆ᳛ᑖ/zX}=,+j+2,aᦪ(ᑣz§0}=..z⚪10ᑖ}4#ᳫ-.ᙢᙠ5#(ᑡHIḄᭆ᳛z1}4#ᳫᐰᙠ#z2}ាᨵ#ᨵ2#ᳫ..z⚪10ᑖ}A-.RS§ḄᑖA0«/(%)=<1+x0,x<0ᡈx>3পᦪ¡ফz"Dz3}஺Ḅᦪ678.£.z⚪10ᑖ}A:¤-.RSz§,஻}ḄὶᔠᑖC஻=1஻:2஻=4஻=5f=00.050.120.150.07f=10.030.100.080.11f=20.070.010.110.10পf¨஻CᔲDEFGªz2}J•஻Ḅᑖ¬EzJ஻}.z⚪10ᑖ}ᨵ10®(ᐸ1°±᳛90%,ᐸ3920%.-.⌱´ᐸ1(+´01µ®(,®¶°±Ḅᭆ᳛·¸ªq,®¹¶°±(ᑣºᩭT°±᳛¼Ḅ1Ḅᭆ᳛C·¸ª½.z⚪12ᑖ})gh¾¿®ÀÁ(3ᨵ4Â.Ãgi#j᪗.>giÂÄÅÆ10ᐗ.q3gj᪗(ᑣ1ᝄÉ100ᐗ(ÊÀÁËÌ.q4Ârgj᪗(ᑣÀÁËÌÊ3⌕ÅÎÏ100ᐗ.q3>Âij᪗Ḅᭆ᳛0.3,3ᙠÐÀÁḄᦈÒḄ78.Ó.z⚪12ᑖ})ᔆÕJḄÖI×Ø᳛5%,)*⌕ÙÚᢇÖI(3Ü895%Ḅᭆ᳛ÝÞᐸᨵ2000#ᔠßØ.à3á¸âÚã·¸ÖIªzäå0z1.28}=0.90,0z1.65}=0.95}ç.z⚪6ᑖ}AHI?Bஹ஺DEFG(èÞéAU8¨஺DEFG.)êᨵ50ë6Õ(ᐸ17ì5*(18ì15*(19ì22*(20ì8*(ᑣ,ê6ÕíîḄ᪵ᙳ.ᓝ.òS)óô᮱ᑁḄ÷({øòS5Â(ᦪù᝞zᓫüå°C}å1820,1834,1831,1816,1824Ꮇÿ
ᡠJ~.b=10,"Ḅ0.95Ḅ.!"0(1.96)=0.975,জ(1.65)=0.95)-1)"^=-(1820+1834+1831+1816+1824)=1825------------------2ᑖ12]-a=0.95,CL—0.05,u==].96--------------------------5ᑖa~2s஺101.96x10b=1°:;5,U^-j==WW=XW—8.77-----0025ᡠ஻Ḅ஺95Ḅ>?1816.23,1833.77@ᓫB"࠷D------10ᑖ)EFGᑖ᪗IJ.1.DDஹ2.DDஹ3.ADஹ4.CDஹ5.CD33

33OᓭᜧR(S)T.1.0.85ஹ2.:U5ஹ3.E(j2)=29ஹ4.0.94ஹ5.3/4Y.Z4[ᳫ]^_ᐭ5[abcᐳᨵ51=625fghijk-------------3ᑖ(1)A=l4[ᳫᐰᙠJ[abopᐳᨵ5fghijk,ᦑPU)=5/625=1/125-----------------------------------------------------5ᑖ(2)5[abc⌱J[_u[ᳫ:v⌱u[ᔜ_Jᳫᨵ=30fxy---------------------------------------------------7ᑖ4[ᳫcz2[_ᙠJ[abo:ᐸ|2[ᔜ_ᙠJ[aboᨵ12fxy}~:B=lាᨵJ[abᨵ2[ᳫpᐳᨵ4X3=360fghijk.ᦑ(2)1)dx=A

342=—•6ᑖ2ব)dx-A[x-ln(l+x)]j13=---(3—In4)=-----1--------------------------------ioᑖln4In4.)"(i)gḄᑖ>(012)-------------------------------2ᑖ(0.390.320.29JnḄᑖ>1245]0.150.230.340.28}P(J=0,஻=1)=0.05H-0)U(=1),ᦑ4Fn------5ᑖ(2)Ḅᑖᑡ>01245810p0.390.030.170.090.110.110.10}~,77)=0x0.39+1x0.03+2x0.17+4x0.09+5x0.11+8x0.11+10x0.10=3.16------10ᑖ)"gFq,ᑣᨵP(I=0,n=1)=P(l=0)P(n=1)P(€=0,n=2)=P(g=o)P(n=2)34

35"¡,OᓭᜧR(S)P(a=i,n=1)=P(=1)P(n=1)P(g=i,n=2)=P(g=i)P(n=2)}~:/¢=0,2=1)/©=0¤=2)/(1=0)U===P©=1¤=2)=P(J=1)0.050.12¥----W----ᦑ€Fn஺0.030.10¦.)"ᵫᐰᭆ᳛ª«¬Bayesª«(¯fbi°±)=0.1X0.9+0.9X0.2=0.27-——5ᑖP(¯fbᩭ³°±᳛´ḄJa)=(0.1X0.9)/0.27=1/3--------------------10ᑖµ.¶4=lᙠ·k¹º»¼»c½᪗p,A0=l4¹¾¿»c½᪗p஺ÀÁU(Aj=0.3;U(A?)=0.7X0.3=0.21;U⊈)=0.72X0.3=0.1472(A,)=0.7;'X0.3=0.1029;ᡝ(A0)=0.7=0.2401-----------------------------------6ᑖᙠÇ5fÈÉÊ:|ḄᦈÌgᑖÍ>90ᐗ:80ᐗ:70ᐗ:60ᐗ:J140ᐗ஺8ᑖ}~,£(^)=0.3x90+0.21x80+0.147x70+0.1029x60+0.2401x(-140)=26.65-------------------ᑖ12Ð.)"Ñ|ÒÓÔÕ஻[Ö×:ᑣ஻Ø2000,ѯᢇÖ×cᔠÛÖ×ᦪgÝÞT⚗ᑖB(n,p),p=0.95.}஻áᜧ:ᦑB(n,p)âãFN(np,npq)-----------4ᑖᵫᩩ×ᨵPᓄ>2000)«1-জ(20*ߟè)=0.95-8ᑖyjnpq\]:Ðc200-np,}0(1.65)=0.95,ᦑ—/—=—1.65,)n=2i23,ᓽÒÓ⌕ÔÕ2123[Ö×.-12ᑖì.í:}AஹBஹC,ᦑP(AC)=P(A)P(C),P(BC)=P(B)P(C),P(AB)=P(A)P(B),P(ABC)=P(A)P(B)P(C).P((AUB)C)=P(ACUBC)=P(AC)+P(BC)—P(ABC)-----2ᑖ=U(A)P(C)+P(B)P(C)-P(4)P(8)P(C)---------------------4ᑖ=[P(A)+P(B)-P(A)P(B)]P(C)=P(AUB)P(C)ᦑAU8Fc.------------------------------------------------------6ᑖRᔁ(~)JஹÁð⚪(ᐳ7ᑖ:ò⚪1ᑖ)1.ÑA,8,C>]^ó×:ᑣAFAuBuCÁõḄ.2.U஺)Áö᝱]^øḄᑖùᦪ:ᑣ/(-©Hl-f஺).3.]^øxFy:ûüz1F-1Ḅᭆ᳛ᙳ>0.5,ᑣþ=y.35

36ÿᓭᜧ()4.ᙳᒴᑖḄᑖᙳᒴᑖ.5.᪵ᙳḄ!"2$%&'(!Ḅ)*+,.6.ᙠ/0Ḅ123l-a789+:ᦪḄ12<=$0>7.ᙠ:ᦪḄᎷABCD8EFḄG᪷IᜓKᎷALM0Ḅ.ஹ⌱K⚪(15ᑖ8R⚪3ᑖ)(1)ABuA,ᑣ7☢ZMḄG஺(a)P(A8)=1-P(A)^(b)P(8—A)=a(8)—a(A)b(c)P(BIA)=P(B)(d)P(A1B)=P(A)(2)dᦣfghijXḄᭆ᳛ᑖna(X=᝕)=4)’(᝕=1,2,•r)Ḅᐙ⌕ᩩv(a)4=(1+A)TyA>0b(b)A—1—|y0<40y(3)A10ᵯḄX,(i=1~10)ᑖ8y£>(XJ=A(i=l~10),ij10ᵯḄᙳyḄ!஺(y)=.(a)Ab(b)0.1Ab(C)0.2Ab(d)10A.(4)A(X”X2,…8X“)n%&X~N(0,l)Ḅr᪵8᜛n᪵ᙳ8$2n᪵!8ᑣᨵ(a)K~N(0,1)b(b)nX~Af(O,l)b(d)(஻-l)X^/£x^~F(l,n-1).(c)X/Si=2(5)A(X1,X28rஹX“)n%&N(஻8(y2)(஻£¤)Ḅr᪵8ᑐn᪵ᙳ8ᑣᙠ%&!cr?Ḅ7ᑡ+,jD8n)*+,jḄ_______oA1஻_A1n(a)erf=—Z(Xj-X)?b(ಔ=--£(x.-x)2b(஻,-=iAi஻A1n(C)(d)b^=£(X,.//)'-஻-1±ஹ®¯⚪(18ᑖ8R⚪3ᑖ)(1)Agh²vA,B³$´µ,yP(4)=0.3,P(ὡ)=0.6,ᑣP(8·)=____________.(2)AghijX¸¹(-2,2)Ḅᙳᒴᑖ8ᑣghijº=X?Ḅᭆ᳛»3¼ᦪn/y(y)=___________.(3)Aghij(XJ)~N(0,22;l,32;0),ᑣᭆ᳛P(|2X—ᓃ21)=36

37"¿,ᓭᜧÀÁÀ4ÁAghij3X,YḄὶᔠᑖÄnÀx,yÁÀ1,0ÁÀ1,1ÁÀ2,0ÁÀ2,1ÁP0.40.2abÅEÀXYÁ=O.8,ᑣcovÀx,yÁ=.À5ÁAÀX],X?,r8*6ÁᩭÍZ᝱ᑖNÀ0,1ÁḄ᪵8y=À£x,.Á2+À£x,.Á2i=lr=4Ï஺=Ð8cY¸¹72ᑖ8EÀÑ2Á=.À6ÁAÒÓÔÕÖ×Ð=X~NÀM8஺2ÁÀᓫÚ^ÛÐÁ8Ü஻=9Ḅ᪵8Þ᪵ᙳß!ᑖànX=6,S2=0.33,ᑣ஻Ḅ123n95%Ḅᓫâ12<=▲n^.äஹ,åæçᵨ⚪À54ᑖ8R⚪9ᑖÁ1.Òᔆᓱëì〈■“ïᐺ”ᵨñ7ò8⚔ôõ10ö÷8ᐸD5÷ùᵨúûஹ2÷üᵨúûஹ3÷ýþÿ.ᑮḄᙢᜫ1ᜫ•.ᒕ9ᡭ2ᵨ"#$ᜫḄ•%ᵨ"#Ḅᭆ᳛.2.)*+,-.X,Y2Ḅὶᔠ567ᦪ..ஹA0I%2K.32MNxOyḄPᐵឋ.3.)*+,-x~u.o,i2.ᙳᒴᑖZ2y~E.I2.ᢣᦪᑖZ2]^_P`abc$z=2x—gḄ567ᦪ/z.Z2.4.klᵯnopᨴrs20tuvᢗlᵯxy᳛z0.0005.|}puxy~᩵Ḅᭆ᳛z0.01.cᵨ᩽▲ᳮ$|}ᔆḄlᵯxyᦪ3uḄᭆ᳛.5.)XḄᭆ᳛ᑖZᑡzX0123J342p3l-p/}l-2p-ᐸp.0

38¿ᓭᜧÁ(ÃÄ)(1)ÆÇᔲÉᔠÊnZḄᦪË1260࠷?(2)ÌḄ᪗ÎÏᔲ2࠷?ÐÑÒᑏ|}Ô.ÕஹÖ×⚪(6ᑖ))*+,-XOgP`abII¶ᦪz3ḄÙÚ(Poisson)ᑖZ.Ö×X+g߶ÙÚᑖZᦪz6.▬⊤᪗η᝱ᑖZᦪ⊤72ᑖZᦪ⊤tᑖZᦪ⊤জ(0.4)=0.6554(3)=7.8154).025(3)=3.1824জ(1.645)=0.950ä02s(3)=9.3480.05ব=2.3534জ(1.960)=0.975ä05(4)=9.448t).05æ=1.8595*3(4)=11.1430(2.0)=0.97720.025æ=2.306᪗η᝱ᑖZᦪ⊤%2ᑖZᦪ⊤tᑖZᦪ⊤0(0.28)=0.6103/aভ=9.488t).025(15)=2.1315জ(1.96)=0.975/.95(4)=0.7110.05(15)=1.7531জ(2.0)=0.9772è3(5)=11.071.025(16)=2.1199জ(2.5)=0.9938n9s(5)=1.1450.05(16)=1.7459—■î⚪îî..⌱ð⚪(b)(a)(b)(d)(c).:ôõ⚪(18ᑖp⚪3ᑖ)ö÷øùᑁzBᔁýᫀÿRI/(477)0')=*ஹ0ᐸ3.0.8446.4.0.1.5.1/3;26.▲6.356.éOêᵨ⚪1.A—ì2ᵨ"#B——ᜫḄkk=1,2,3ᑖ⊤"#ᵨ%&'(ᵨ%&')*+,.kP(A)=VP(1)2(A|1)=1•5+2•58h'2C810Cl5C836Ic23X3P(:A)=P(B1)P(A|BJ/P(A)==⌼/P(A)=?+@=3•ZCJO30o938

39EᓭᜧHIJKL(1)A=1/4.f(l/4)dy=x/202/2)dx=4/3,£(y)=\dxO(y/4)dy=0,J()JoJ-.r£(XK)=Cxdx['(y/4)dy=0,cos(X,Y)=E(XY)-£(%)£(7)=0JoJ-Jᡠdx5yefᐵ.10o3-/x(x)=<6(y)=,0ᐸoy<0fzব=iJx(x)/y(2x-Z)dx05nkzmḄᑖnoo522x-z>0x>z/2OeY2)dx=eZ(ie-2)/2z3)=1-P(y<3)»l-O/«1-0(2)=0.0228.IJ1-5x10-6J85.প?=^X,=16/8=2,E(X)=3—4p=V,/=1k஻Ḅp=(3-X)/4=l/4.39

40'EᓭᜧH(JK)(2)ᯠᦪ8L(P)=RP(X=x)=P(X=O)[P(X=l)]2P(X=2)[P(X=3)]4ii=\=4p(l—p)2(l—2p)4InL(p)=ln4+61np+21n(l-p)+41n(l-2p)[InLCp)]^----------=0,n12P2—14p+3=0p1-pi-2p=>p=(7±V13)/12.ᵫ0f-1)=t(3)=3.1824.0025ττ=1267_µ=3836ு3.1824,·ᙠ°±²ᑁ'113.65/74ᦑ°±ºᎷs”()'ᓽe½¾¿ÀÁᔠÃÄḄᦪÅ1260࠷.(2)ÇḄᎷsH:o-<2,H:a>2atᵨḄ®¯32=(஻È?S~32(”_]),6ro°±²%->Za(«-1)=Zo,O5(3)=7.815Zo=40/4=10ு7.815,·ᙠ°±²ᑁ'ᦑ°±ºᎷsH(),ᓽe½¾ʦḄ᪗ÌÍeÎÏ2࠷.Ðஹ@Ñ⚪(6ᑖ)ᵫ⚪s2(X=m)=Ô*3,2(=")=2_*3,஻'m=0,1,2,•mln!40

41EᓭᜧH(JK)P(X+Y=i)=£p(x=k,Y=i_k)=£p(x=k)P(Y=i-k)k=Qk=0=£ᦻ/.^^e-3^e-6-Y--—3".3£Ø(i-ky.i'.f^k\(i-ky.j6=e"(3+3y'”0,1,2,…ᡠdx+yÚÛÜÝÞᑖÄ'ßᦪ6.ᑨá⚪(10ᑖ'â⚪2ᑖ)1.ᙠãᐺᭆæḄçèé'2(A)=oX{êXAëeì½íî.()2.ïðæçèñ¯Ḅòóᦪ/(X)5ᐸᑖÄᦪ2(X)fôõö.()3.÷çèñ¯x5øù'{úÛÜ஻=0ûḄ(0,1)ᑖÄ'ᑣx=y.()4.sXýᦣæçèñ¯'{ÿᙠ
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ᖪ8ᦪᙠ508ᑮ708=>Ḅᭆ᳛.4.BCDX~N(஻(T2),(X1,X2X“)CDXḄ2E᪵G.HIᦪ⊟KফX,-MbḄOPQ/.i=l5.(1)᪷TUḄVᔆXYḄᱯ[\]Ḅᢚ_`X~N(஻cr2)(ᓫefkg).ijb=8kg,lᔆXYḄ2ᜧᢇᱯ[\]*opqr10E᪵st᪵Gᙳv7=575.2kg.wxᢇᱯ[\]Ḅyᙳᢚ_`zᔲ|$570kg?(a=5%)(2)ijᙠIᩩ8᝱ᑖN(஻O.O482).qr5E᪵stᐸf1.31,1.55,1.34,1.40,1.45.wxᜩḄḄCD$ᔲIᵨa=10%ᎷB.ஹ⚪(7ᑖ)BopX,y,Z%&'(2ᑭᑖ8(1,P).opX+Z%&'(.■.ᑨ_⚪1.$.ᙠ¢£ᭆ¤*¥⚪“P(A)=O¦§¦A$Mz¨©8”$Mᡂ(Ḅ.2.¬.ᦋ®¯ᦪ/*)ᙠE²³´Ḅ¯ᦪvMµᦋᑖ¯ᦪF(x)Ḅrv.3.¬.ᵫ⚪Bᩩ8ztp(x=y)=o.82,᪷GM¨·x=y.OP4.¬.ᵫ⚪Bᩩ8zzº\+஻*¼½ᦈ¿ᓽE(X)ÁÂᙠ.Jt=l5.$.ᵫᐵÆÇZa+Z/?(ÉÇÊ"v)z˺.Ì.⌱Î⚪1.(a)2.(d)3.(b)4.(c)5.(d).Ð.ÑÒ⚪ÓÔn(y/3)])y>01.19/396.2.,(>')=4>.3.0.9772.Y0y<0-„τfl/(2x)-x

44Ýᓭᜧß(à)./0⚪1.A—âãä|$ᔠæḄ©8BqãḄYᔠæḄ©8.P(A)=P(B)P(A\B)+P(5)P(A|B)=0.96x0.98+0.04x0.05=0.9428,P(ᓽA)=P(B)P(A|B)/P(A)=0.9408/0.9428=0.998.í-(")x>Q,y>Q2.ì2f(x,y)=<0ᐸÜzீoÙF(z)=o,ó/(z)=oôz>oÙ,7Z(z-3x)/2Fzব=P(3X+2Y0fzn='0,z<0x>0pe-f,yy>0ìÌfx(x)=<4(y)=0ᐸÜ0ᐸz40f(z)=0zz>0/(z)=i4(x)Al(z-3x)/2]dxZ5…J1e-""2)203//-22ᡠ"A/J(e"_e*/2),7ு஺fz(z)~<3஻—220,z<0Z=3X+2YX=(Z-2W)/3_1/3-2/32+,-W=YY=W013z-2w|J|=g?@AB0123(Z,W)Ḅὶᔠ789g(z,w)=/3'=2ᡠ"/z(Z)=£g(z,w)dw=|£44

45DᓭᜧG(HI)———(@"3_e-஻z/2)Z>03/Z-223.-X,9K/ᕜḄ├N3i=1,2,…,52X,~P(1),ᑣRSḄ├N3952Y=YXi>E(Y)=52,O(Y)=52.i=\ᵫWXYᑖ[Ḅ\᩽▲_ᳮᡠaᭆ᳛9-2Y-52P(50

46",DᓭᜧG(HI)IU];70=065=2.06>1.96,ᙠ|}~ᑁ118/V10ᦑ|}Ꮇ-”()ᓽ9ᙳᢚ9570kg.222(2)⌕rsḄᎷ-9H:a=0.048,H]0.04805Z(x,.-X)22rsᵨḄyz3Z=——-------%2(஻-1),0-024=|}~9z>-1)=Zo.05()9.488ᡈ/9.488,ᙠ|}~ᑁ(ᦑ|}Ꮇ-”0,ᓽ9ᜧḄ8Ḅ.⚪Rᵫ⚪-¡x1x+r0|i22PqpPq,2Pqpp(x+y=o,z=o)=/=p(x+y=o)p(z=o)p(x+y=o,z=1)=஻/=£(X+y=o)p(z=1)p(x+y=i,z=o)=2஻q2=p(x+y=1)£(z=o)¤p(x+y=i,z=1)=2Pq2=p(x+y=I)P(Z=1)P(X+y=2,Z=0)=p/=p(x+y=2)P(Z=0)p(x+y=2,z=1)=p?=p(x+y=2)p(z=1).ᡠ"x+y¥zjkWX.¦ᵫ⚪-§¨x+y¥zḄὶᔠᑖ[46

47DᓭᜧG(HI)ὶᔠᭆ᳛©▣\«¬ᡈ¬ᑡᐗ°±²ᡂ´µ,ᦑᭆ᳛©▣Ḅ¶·¸1,ᡠ"X+Y¥ZjkWX.¹º⚪(ᐳ7ᑖ,¼⚪1ᑖ)1.-Aஹ8¹01¿ÀP(A)=O,ᑣArBjkWX.()2.£(x)¹᝱0123Ḅᑖ[ÂᦪᑣF(-X)H1-P(X).()3.¦Äᙳᒴᑖ[ḄÆÇᑖ[ȹᙳᒴᑖ[.()4.X¥yjkWXÉÊËÌᢣᦪᑖ[E(A),ᑣX+y~£(22).()5.E(xy)=E(x)E(y)¹x¥yjkWXḄÎ⌕eºᐙᑖḄᩩÀ.()6.᪵ÒᙳÓḄÔ2¹ÕÖ஻2Ḅ×ØÙz.()7.ᙠᎷ-rs\|}~ḄÚÛ¹᪷ÝᜓßᎷ-eà_Ḅ.()¦.⌱ß⚪(15ᑖ¼⚪3ᑖ)1.-0123X~N(O,1),±ã_Ḅa(0Z")=a.è£([x|)P(X—yKl)=l/2.1n3.-0123X1,X2Rஹx“WXYᑖ[É9a?ுo.óy=-£Xj,ᑣ.n,=1(A)Cov{X^Y)=(y2In-ô,7)=cr2;(C)£)(%,+r)=(/i+2)cr2/n(D)-K)=(n+l)cr2//1.:4.-X”X2,…X”¹ᩭú᝱N(஻,l)ḄRûüᓫ01᪵ÒX,S2ᑖþ9᪵ÒᙳÓ¥᪵ᩈ
,ᑣ.(A)X~2V(O,1)(B)^(X,-X)2~/2(«-1)i=1(C)£஻)2(D)ߟi=iS/yn—147

48ᓭᜧ!"#5.ᙠ"o()Ꮇ+,(ᜓ.Ꮇ+ḄᎷ+012,34℉ឋ78(9,ᑣ.A#P;<“0I/ᡂA#=a;B
P;2X-y#=l,ᑣ᜛=.5.+xyX~N஻,cf2#,(|Z}ᦪ,ᑣ஻Ḅ~(1-aḄ~(V+X+X#26.+X”X2,X3,X4ᩭ᝱xyN0,9#ḄᓫUV᪵,J=——%lmᑖ3Xτoᑏᵫ#..⚪54ᑖ,Q⚪9ᑖ#1.ᵬஹஹ3nnjA}ᭆ᳛£¤ᦪᳮ¦§ὃ©,ª«¬Ḅᭆ᳛ᑖ(0.4,0.3,0.5,1#®ាᨵTnª«¬Ḅᭆ᳛2#᝞²Y³Z⍝µ3n2ᨵ2ª«¬,®ᐸ2•nḄᭆ᳛.2.+9¸UV^_X,y#Ḅὶᔠ»¼ᦪ/x,y#=<¾J,®0,ᐸ¿পx,yḄÁ»¼ᦪÃফÅx=i/3,yḄᩩX»¼ᦪ/Çx#'|x=1/3#3#PCX+K<1#.'le-2x-y,x>0,>>>03.+9¸UV^_X,y#Ḅὶᔠ»¼ᦪ/x,y#=j,,,[0,ᐸ¿®Z=max{X,Y}Ḅ»¼ᦪ.4ÑᔆÓÔÑÔÕ1000X,ᐸÖ¬(P=2000ᐗ/X,ᐸØᵨÚÛXᓫÃᜩ#Ḅ48

49ᓭᜧ(!")I~20000(^~365)x>365F/Vஹ—J20000eᑖo»(ß,j0x<365àᵫÑá◅ãä(ᐸå_æçá◅Ãᔆᔣá◅ãäéáêᨴᐗ/X,3QXÔÕ3ÚÛìí1095ᜧ(3î),ᑣᵫá◅ãäᢥ)Öðñ2000ᐗ/X.©ᵫ2ò᩽▲õᳮ(1)3áêö=100ᐗ/X,á◅ãä÷Ḅᭆ᳛ø(2)©ùõáêö,Øá◅ãä÷Ḅᭆ᳛ªúû1%.“0365஺096,0(1.45)=0.926,জ(1.61)=0.946,জ(2.33)=0.99))o(6+1)(%-5)50),0ᐸ¿ᐸ2eᙳ(|Z}ᦪ,®oḄþÿ
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#500&᪗"'()*+10&.-ᜩ/01#234ᘤ5ᔲ7089:ᒹ;Ḅ<=>9@AB=499,§2=16.032.JKᜩᒹ085ᔲ7(a=0.05)?ᓽ34(1)H:/J=500,:*500R(2)%:441()2,&>IO?.0X0஺25(8)=2.306,/.(9)=2.262.2(8)=17.535,.2(9)=19.0230025Zoo25Zoo25‘15(8)=1.8595,஺05(9)=1.83312(8)=15.5O7,2(9)=16.919Zoo5ZoO5`.ab⚪(6ᑖ)de4ஹBஹChijklmnde஺jkabXP(A)+P(B)+P(C)<2+P(D).■,5s⚪55ss5s5.⌱u⚪CBABC.x.yz⚪1.0.5R2..0.331R3.5/9R4.7/8(ᡈ0.875)R_S_s5.(X---j=t(rt-l),X+—j=t(H-1)):aayln2vn26.F(1,1)..⚪i.XAaARᑖ⊤“ᵬ(”ஹ“(”ஹ“(”xdeᵫ⚪4,4,4A⊤“ាᨵ2(”ᑣ49

50ᓭᜧ¢£¤¥A=4AA3U4A2A3U442A32(1)0(A)=P(444)+¦(A&4)+P(AA2A3)=0.4x0.3x0.54-0.4x0.7x0.5+0.6x0.3x0.5=0.29(2)P(4A2%UAA2A31A)="A"'©'_0.4x0.3x0.5+0.6x0.3x0.502915-292.Xপ¬00£>¥=,Ry>0/x(x)=Jox<0y<0B(Z)=P{max(X,Y)Wz}=P{XKz,yீz}=P{X0/zQ)=0ᐸ²50

51Ìᓭᜧ¢(¤)=஺-365)x>3654.XXḄᑖÍᦪF(x)=0,x<365Ï5P(X<1095)=l-e-°0365«0.04N="1000eÐÑ<ÒÓÔÏ1095ḄÐÑeᦪ"ஹy="Ö◅ØÙḄᑭÛ“ᑣ"B(1000,0.04),y=1000ÜÝ-2000N,ᵫ<Þ᩽▲ᳮN~N(40,6.2?),Ï5(1)áÖâ6=100ᐗ/eä/'Ö◅ØÙåæ”={çW0}={N250}N—401()P{Ö◅ØÙåæ}=èç<0}=P{N250}=P{------>—}஺1¹জ(1.61)=0.0546.26.2(2)áÖâ#ᐘ,ᑣ“Ö◅ØÙåæ”={1<()}={NN0.51}/A—»ߟ.IN_400.5ᓃ—400.5/?j_40P{Önr◅rØÙæ}=P{N20.5%}=P{-------->-——}~1-0>(-o——)<0.016.26.26.2ᦑ<(ì)—ìí3nP>2x(40+6.2x2.33)=108.89(ᐗ)o5.XEX=[x(8+l)(x—5)%x=fM(x-5Ð=6-£(X-5/+IJX=6--^-^î1ᦑ஺Ḅï
#0=——=-26—XᯠÍᦪL(6)=flf(;6)=(஺+l)nfla—5)0,Xii=\i=]InL(e)=஻ln(l+e)+e£ln(x-5);1=1dInL(B)n..-----------=-------+>ln(x-5)=0ndd1+0W;஺Ḅ᩽ᜧᯠ
#4=---------------------1£ln(X,-5)6.Xপ"0:஻=500%X஻஺500.51

52ðᓭᜧ¢(¤)áHᡂò
T=Xó50°~r(8).o°S/3c,,X-500,ᵫᜓuᎷö÷øḄùú#஺=I----------1>A,S/38ᵫ¦{TeOI40}=P{τTl>Aτ“0}=4A=^.025()=2.306.ᦑö÷ø#O={ITI>2.306}.3ûᐭᦪýATḄþÿ"=———=-0.187,஺ᦑ”().16.03(2)H:cr2<100,/7,:100.08s2ᵫᜓᎷ“IḄ஺={>A}.Qc2oc2Oc2ᙠ“0"஺24100ᡂ$Ḅ%&'p{—>A}ீp{)ுA}஺ᵫ72==~72(8),100bbQC2QC2,A=-05.=15.507,ᑣP{—>15.507)-஺8)}=0.05.100(TOc2ᦑ஺={01>15.507}.1002ᐭᦪ568*ᵯ/1=20.56eD,ᦑ9“().100°;.(6ᑖ)=>"ᵫ⚪ᩩA48CuOnP(ABC)KP(£>),P(A)+P(B)~P(AB)<1nP(A)+P(6)<1+P(AB)=>P(A)+P(B)+P(C)W1+P(AB)+P(C)=1+P(ABUC)+P(ABC)<2+P(ABC)<2+P(D)Rᔁ(=)1.BC⚪(7ᑖD⚪1ᑖ)1.P(A)=0,ᑣEFGA4HIEFGA51JKLM$.()2.NOEFPQXḄRSTᦪ/(x)ᐸᑖVTᦪf(x)WXKLY1ZJ.()52

53"[,\ᓭᜧ_(`a)3.cXYfB᪗hi᝱EFPQᑣX+l~N(0,2).()4.ᨵᑖVs"P{X=(—I)""/"}=1/2",(஻=1,2,…)ᑣXḄz{|ᙠ.()5.EFPQ~ᑡ*],*2/1*“1KLM$ᙳᦪḄᢣᦪᑖVᭆ᳛ᦈ4.()6.ḄS1-aḄḄZS.()7.ᙠᎷ¡¢℉ឋ¥¦aBᢣ§(஻o|஻oᎷ)=1-a.()⌱⚪(15ᑖD⚪3ᑖ)1.NOEFPQXḄRSTᦪ«¬/(x)=/(-%),§(x)BXḄᑖVTᦪᑣP(|x|>2004)=.(A)2-£(2004)±(B)2F(2004)-1±(C)l-2F(2004)±(£))2[l-F(2004)].2.)·EFPQ(X,y)G0ḄᙳᒴᑖVGḄᵫ»¼y=½2y=xᡠ¿ÀMX,Y)Ḅὶᔠᭆ᳛RSTᦪ.[6(x,y)eG1/6,(x,y)eG(A)/(ÄÅÆ(B)/(x,y)=ᐸÈ;0,ᐸȱ2(x,y)eG1/2(x,y)eG(Q/ay)=0(D)f(x,y)=\ᐸÈ;ᐸÈ.3.(X,y)~N(0,0.5;0,0.5;0),Z=X—y,ᑣÍΣ)(|z|)=.(A)0±(B)1±(C)1+2/%±(D)\-2/7T.4.-ÐX~8(l,p),X1,X2/-,X”BᩭÔ-ÐḄ᪵ÖV᪵ÖᙳᑣP(T=k/஻)=.(A)p(B)/(1-p)i±(C)C"p"l-p)i"(D)C(l-p?*.5.-ÐX~N(஻cr2),஻Wᦪ᪵ÖX|,X2,…X”ḄÍÎS2,ÞᎷH:a>2,H:a<2,¥¦aḄB.al(A)%?4%à/2(஻11)±(C)/(஺)z2

54"[,\ᓭᜧ_(`a)ä.åæ⚪(15ᑖD⚪3ᑖ)1.ç§(A)=0.7,7(8)=0.4,§(è)=0.8,ᑣ§(é44ê)=.2.EFPQXlKLM$fë0,1ì0ḄᙳᒴᑖVᑣZ=|X-l|ḄᑖVTᦪFzízî=<3.E(X)=l,E(y)=2,D(X)=l,O(y)=4,ñxy=06Z=(2X—y+l)2,ᑣᐸᦪ_z{E(Z)=.4.EFPQX~N(஻Cf2),ᵫᑗôõö÷øᭆ᳛§(|x22஺)Ḅ,ù.5.XrX2,…X”BᩭÔ-Ðú2(஻)ᑖVḄ᪵ÖûB᪵ÖᙳᑣE(V)=,£)(%)=.ü.ý⚪(57ᑖþ)⚪D⚪9ᑖ
⚪⚪10ᑖ)1.ᳫᨵ6ᳫ
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ᐳ
(1)!"#$%ᑮᳫḄᭆ᳛*(2),-ᐸ/01ᳫ
!"231ᳫḄᭆ᳛.2.“ᜩᙢ”8⏀ᔳ;<=ᨵᔳ>7@
ABᐰDḼ
Fᨵ2GHIJᩭLMᐭO
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!"[\ᕒ⚜_cdḄᭆ᳛.3.fLMghXᙠ(0,஺)lLMᙢm
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cç¡MᘤḄÖéêë
LMᙢ6×
ì᪵ËᙳmX=495.3ä
᪵Ëᙳí°s=13.74ä.²"îçïYZ஻Xí°cr?ᩭᑨòᒹÔMóᜩḄÖé1ᔲõ(a=0.05)?ö.«÷⚪(6ᑖ)fA,8,C1åB,HúûüḄLMýþ
ÈP(A)=P(B)=P(C)=254

55@ᓭᜧ()஺Ḅᨬᜧ1/2.▬᝱ᑖஹfᑖஹ,2ᑖᦪ⊤&0(1.285)=0.9,জ(1.645)=0.95,<&(1.96)=0.975,জ(2.33)=0.99%025(5)=2.5706,%.025(6)=2.4469,/(5)=2.0150,^(6)=1.9432005005ZO.O(5)=H.071,ZO.O(6)=12.592,1.7ম=12.833,13য=14.44955•.;<⚪;;<<<;<.>.⌱@⚪DADCB.A.BC⚪'0,z<01.7/8F2.Fy(y)=-2z-z2,0l3.4.2I4.0J0.25KLI5.஻2.N.OP⚪1.QFR4=STiVWXᳫZ,i=l,2.পRC=ST>V\WXᳫZ,ᨵ464-X-=一P(C)=P(A>L)=PCA^CA,IA)W9a7/30&F15(2)RbcD=SdeᐸgK;XᳫZ,£=SᐸgK;Xᳫijk;XᳫZP(ED)=P(A4)=P(A)P(4IA,)=^x|=1P(D)=p(44)+P(4H)+P(A4)1--=-+P(A)P(&IA)+PভP(4IA)1644613=—Hx—Ix—=310910915P(ED)_1/3_5P(EIO)=P(£))-13/15-13Qv>Rbc8=Swjgxyᨵj;XᳫZ,A=Swjz;XᳫZ,ᑣAuB,P(AB)_P(A)_Cj/C^1/30=ᡠᩩcᭆ᳛=P(A|B)==5/13.P(B)(CFCF+CI)/-8/15+1/32.QFᑖ55

56ᓭᜧX012345p6/215/214/213/214/215/21(01234r[1/34/151/52/151/15)E(X)=35/21=1.67,P{X>2)=10/21»0.476.—ᵪ10cx<஺x)=஺)஺)=|a(a-x)0,ᐸyw(0,a)A(><)="aa-y0,ᐸ4.QX~B(w,p),E(X)=np,O(X)=஻p(l_p),P{l—-pl<0.1}>0.95.nᨵg᩽▲ᳮP{l—-pl<0.1}=P{}ᓺI0.9510jp(l-p)=>0(—w)>0.97510jp(l-p)=>n>19.62p(l-/?)g(P)=P(l-P)g'(p)=l-2P=0,p=l/2,g=1/419.62p(l-p)[96.4]+l=97.81—5.QFE(X2)=[xx2/ydx=2஻,O56

57'ᓭᜧ()-1n᩽ᜧ¢ᯠO^=-Yix,I.«,=i6.QF5=495.3,s=13.74,52=188.788,(1)§¨©ªᎷRH:஻=500;%500()a=0.05,?(5)=2.5706,W=(-oo,-2.5706)u(2.5706,+oo)0025,,lx-50011495.3-5001³””_„11T7^1=——-——=————x2.4495«0.8379eIV,[0,4098eW]¹º"().4n(2)§¨©ªᎷRH:a2=100;H,:(r2>100na=0.05,705(5)=1161,½¾¿W=(11.071,+8),2(n-l),r5x188.788³Z=----2—=———=9439ÀW,¹ºÁᘤÃÄÅ.oer஺100Æ.⚪(6ᑖ)(ABuC)u(AuC)=P(ABuC)4P(AuC)==>P(AB)+P(C)-P(ABC)<Ç(A)+P(C)-P(AC)nÇ(A)P(B)+P(C)4P(A)+P(C)—P(A)Ç(C)ᓽp~p<1p-pz=>p-lp2>0QÉÊËÌWpw[0,1/2],ᡠÏÐḄᨬᜧ1/2.᪗Ò᝱ᑖḄᑖÓᦪ0(1.04)=0.8508,জ(1.29)=0.9015,0(1.96)=0.9750,জ(2.06)=0.98030(2.17)=0.9850,জ(2.33)=0.9901,0(2.58)=0.9951,0(3.1)=0.9990tᑖᦪ⊤:25(4)=2.78,Z(5)=2.57,Z(4)=2.13,Z(5)=2.02]00025005o05Rᔁ({).⌱@⚪(Õ⚪5ᑖᐳ20ᑖ)1ஹ×ÀØ>bcAÙB(A)ÚABWজᑣA,BÛÜ஺(B)ÚABHজᑣA,BᨵÝÛÜ஺(C)ÚAB=OMPJA,BÛÜ஺(D)ÚAB=(I>ᑣA,BÊÛÜ஺()2ஹRᙠÕVáªgbcAdâḄᭆ᳛p(OVpVl),q=l—p,ᑣnVÛÜäáªgbcAxydâ•VḄᭆ57

58ᓭᜧ()᳛;nnnnA.pB.qC.1—pD.1—q()3ஹåÁᔣ(J,çè>é᝱ᑖᑣ4஻Ḅêᐵìᦪ0=0;஻ÛÜḄ(A)ᐙᑖᩩc஺(B)7⌕ᩩc஺(C)ᐙᑖ7⌕ᩩc஺(D)ò<ᐙᑖk<7⌕ᩩc஺()4ஹRåÁbcAஹBïð8UAᑡôõÊᡂÜḄ;(A)P(Au8)=P(A)஺(B)P(B)ஹBC⚪(ᙠ÷ᑡᔜ⚪gùᨬាûḄQüBᑏᙠþÿ
Ḅᜐ)(⚪5ᑖᐳ25ᑖ)1ஹP(A)=0.4,P(6)=0.3,P(Au8)=0.6,ᑣP(A)=,2ஹ!"#X%YḄ'ᐵ)ᦪ+0.5,EX=EY=0,EX2=EY2=2,ᑣE(X+Y)J____஺3ஹg~N(O,l),6789:;0,1<Ḅᙳᒴᑖ?@4A஻'CDEFIj(a,n)ḄὶᔠMNOᦪ+4ஹ!"#J~8(஻,p)K)=3,0(4)=1.2,FUnQ15ஹ(4,7)~N(஻],஻2TcrTcrTTr)=N<0,0T9,9T-),ᑣ2D(J-஻)=_________________________Qஹ(10ᑖ)ᨵ20\ᳫ^_`abᐸdᨵe\^+fg^+hijabklmᑖ+enop஺qr(1)efg^ᑖᙠtunḄᭆ᳛஺(2)efg^ᑖᙠxtnḄᭆ᳛஺yஹ(10ᑖ)z◅|}Ḅὁz◅uᨵ1_`40ᐗ஺ὁ|}2000ᐗ஺ὁ᳛+0.017,qrz◅|}ᙠlz◅dḄᭆ᳛஺ஹ(15ᑖ)#᮱ᑁḄN#5lᦪ᝞(ᓫ஺01820,1834,1831,1816,1824Ꮇ#ᡠ¢NX~N(UQ2)O(1)r£¤N¥¦”Ḅ0.95Ḅ¨©9:஺(2)ᔆ
«᮱ᑁḄN+1830஺¬ᙠ℉ឋ°±a=0.05²³\´µ஺¶ஹ(15ᑖ)£¤XḄᭆ᳛MN+2/2"®x>0,/(x)=<0x<0ᐸde>o½¾¿_ᦪ஺8£¤xdÁÂÃᓫ!᪵X1,X2x.(1)r஺Ḅ᩽ᜧÇᯠÉÊ158

59ËᓭᜧÍ(Î)(2)r஺Ḅᑖ?Oᦪ£(x);eA(3)ѵ஺½ᔲᐹᨵÔÕឋ஺Öஹ(5ᑖ)u\ᦪᦻØdata,txt,Û½Í▾2006ÝÞßàὃᦪÍᡂã஺ᦻØᨵnᩩåæçèᒹêëìஹᦪÍ,ᵨTabðᑖ◞஺qᵨòÍóḄôØdḄOᦪᡈóö÷᝞ørù☢ᔜ\üÊ#(⌕rᑏ÷OᦪᡈóöḄìÿ
Ḅ)஺ᦪḄᙳᡂஹஹ10ḄᑖᦪஹᦪRᔁ(H)ஹ⌱⚪(#$⚪3ᑖ&ᐳ24ᑖ)1.Ꮇ-./A1B34ᑣᨵP(B[A)=1஺(A)AuB;(B)P(BIA)=O>(0AnB>(D)AABᯠ./஺2.A,BAEFG./&ᑣHᑡᔜKLMNḄA.(A)(AuB)-B=A;(B)(A-B)uB=A;(C)(AuB)-Be:A;(D)(A-B)uBuA஺3.-TUVWXYY[\]^&ᐸᑖ`ᑡᑖab(1-n(1-nX~(0.50.5J(0.50.5JᑣHᑡᔜeMNḄA஺ভX=Y;gP(X=Y)=஺যP(X=Y)4;hP(X=Y)=E4.-TUVWXḄijkᦪbf(X)=——G&ᑣY=2XḄijkᦪb_7t(l+X")2112(A)--------------------•(R)---------------------,(t)--------------•(D)--------------------ji(4+y2)ᐔ(4+y?)'ᐔ(1+4&)'n(l+y2)5.-TUVWX,Y34D(X+Y)=D(X-Y),ᑣBᨵ_______஺(A)X,Y[ᐵ;(B)X,Y]^>(C)D(Y)=0;(D)D(XY)=0஺6.-X1,X2&&X9[\]^&~E(Xi)=l,D(Xj)=l(i=L--,9),ᑣV£>o,ᨵ919(A)P{ZX1<8}>l-8~2;(B)P{<8}>i=lyi=i99(C)P{ZX91-E-2;(D)P{^Xi-9<£}>l-9£-2i=li=I7.X~B(n,p),E(X)=2.4,D(X)=L44,ᑣG⚗ᑖ`Ḅᦪb59

60'ᓭᜧ()(A)n=4,p=0.6;(B)n=6,p=0.4;(On=8,p=0.3;(D)n--24,p=0.1஺8.-X,1X2bEF[\]^ḄTUVW&Ḅᭆ᳛ijkᦪᑖabf](x)1f2(x),ᑖ`kᦪᑖabF,(x)1F(x),ᑣHᑡᔜKLMNḄA஺2(A)f,(x)+f(x)Bb£TUVWḄijkᦪ>2(B)f](x)Xf2(X)Bb£TUVWḄijkᦪ;(C)F](x)+F(X)Bb£TUVWḄᑖ`kᦪ;2(D)ὡ(x)XF(X)Bb£TUVWḄᑖ`kᦪ஺2Gஹ(8ᑖ)¥¦Lᨵ10ᳫ&ᐸL4¨ᳫ&4©ᳫ&2ªᳫ஺«¬¥LTU3ᳫ&®(1)ᑮḄᳫLា±²ᨵ¨ᳫḄᭆ᳛;(2)ᑮḄᳫL³´²ᨵ¨ᳫḄᭆ᳛஺µஹ(8ᑖ)¶⚩¸¦&ᙠ⚩¸¦ºᦪ»1b7Ḅᩩ/H&®ᐸL⚩b1ºḄᩩ/ᭆ᳛஺½ஹ(8ᑖ)¾Lᨵ5ᳫ&¿Àb1,2,3,4,5஺«¬LÁ3ᳫ&ÂX⊤ÄḄ3ᳫLḄᨬ$Àṹ&Ç®XḄᑖ`ᑡ஺Èஹ(10ᑖ)-TUVWXḄijkᦪb®TUVWY=X?+1Ḅᑖ`kᦪYijkᦪ஺Éஹ(8ᑖ)-TUᔣW(X,Y)Ḅᭆ᳛ijkᦪb'3,ஹ—xy',04â&জ(x)=l)஺ãஹ(10ᑖ)-äåXæ¬çèᑖ`&ᓽP{X=k}=(l-p)k-'p,k=l,2,…ᐸL0

61ᓭᜧ()öஹ(10ᑖ)ᙠM᝱äåN(R,1)LìîWb100Ḅ᪵ð&÷õøí᪵ðᙳÜḄòùÜú=5.32,Çᙠû℉ឋþa=0.01IᎷH஺pi=5,H]:H5(ᐸজ(2.57)=0.995,জ(2.33)=0.99)஺(6ᑖ)!"#$%&"'ᦪX*+,ᦪ-A.(k>0)Ḅ23ᑖ4567⌶9:ᨵ'&"஺<"&=>?@ᙠ⌶B"Ḅᭆ᳛-p(00)=_______.x+2x+2½.(Ó⚪10ᑖ)Ô4sᳫᙢ{ᙠ5sÕÖ5RBᑡhiḄᭆ᳛(1)4sᳫᐰᙠsÕÖØ(2)ាᨵsÕᨵ2sᳫ.Ú.(Ó⚪10ᑖ)fḄᑖ4ÎÏ-AÜ0«/(%)=<1+x0,Üx<0ᡈx>361

62àᓭᜧ¨ãäåæã1æRÐᦪ4;ã2æRᡝã*1æØã3æRfḄᦪ¨©ª.r.ãÓ⚪10ᑖæ«èã6,஻æḄὶᔠᑖ4஻=1n=2஻=4஻=56=00.050.120.150.07f=10.030.100.080.11f=20.070.010.110.1()ã1æJG஻ᔲIJKLêã2æR4ëḄᑖ4ìEãU஻æØí.ãÓ⚪10ᑖæᨵ10Õî5ᐸ1Õïð᳛-90%,ᐸ¦9Õ-20%.⌱ᐸ1Õ5+¤1òî5¢înïðḄᭆ᳛-óôêÈ¢înïð5ᑣõᩭ³ïð᳛÷Ḅ1ÕḄᭆ᳛óôêø.ãÓ⚪12ᑖæÀÁ,ùîúû5¦ᨵ4üýÀÂsÃ᪗.=ÀÂüþÿ10ᐗ.᪗ᑣᝄ100ᐗ.4᪗ᑣ⌕100ᐗ.᪗Ḅᭆ᳛"0.3,&ᙠ(Ḅᦈ*Ḅ+,.-../⚪12ᑖ345ᔆ78Ḅ9:;<᳛"5%,4?⌕@ABᢇ9:D,E95%Ḅᭆ᳛GHᐸᨵ2000KᔠM<.NOPQARSP9:T.UV0.1.283=0.90,জ.1.653=0.953[../⚪6ᑖ3\]:4Bஹ஺_`abcHdAU8gC_`ab.4iᨵ50jk7ᐸ17m5?18m15?19m22?20m8?ᑣnik7opḄ᪵/ᙳs".ᓝ.uv4wx᮱ᑁḄ{|}~uv5ᦪ᝞.ᓫVᓃ3V1820,1834,1831,1816,1824Ꮇ}~uvᡠ{|N.஻,b23.b=10,&{|s஻Ḅ0.95Ḅ..UV0(1.96)=0.975,0(1.65)=0.95)ᭆ᳛gᦪᳮBᫀ.1.(1)),2.(D)ஹ3.(A)ஹ4.(C),5.(C).1.0.85ஹ2.᮱5ஹ3.£(^2)=29,4.0.94ஹ5.3/4£.¤4Kᳫ¦§¨ᐭ5Kª«ᐳᨵ5'=625®¯°±²³-------------3ᑖ.13A=µ4KᳫᐰᙠBKª«·¸ᐳᨵ5®¯°±²³,ᦑº஺3=5/625=1/125-----------------------------------------------------5ᑖ.235Kª«⌱BK¨¼Kᳫ½⌱¼Kᔜ¨BᳫᨵCjCÀ=30®ÁÂBB7ᑖ4KᳫÃ2K¨ᙠBKª«·ᐸ2Kᔜ¨ᙠBKª«·ᨵ12®ÁÂÄ(B=µាᨵKª«ᨵ2Kᳫ¸ᐳᨵ4X3=360®¯°±²³.ᦑ஺ÈÉÉ10ᑖj/(x)dx=^Y-dx=AIn4,A=p-Ê.ËVপ3ᑖ-00062

63Òᓭᜧk(}Õ)(2)º©<1)==Aln2=-■6ᑖ2oo3A(3)£16)=xf(x)dx=j_—dx=A[x-ln(l+x)]^-co013=---(3—In4)=-----1-----------------------------ioᑖIn4In4ß.ËV(1)Ḅàáᑖâ"(012)-------------------------------2ᑖ(0.390.320.29JnḄàáᑖâ"C1245ஹ--------------------------4ᑖ10.150.230.340.28ÀfclP(|=0,7À=1)=0.05wP(J=0)P(7=1),ᦑègné_`ab------5ᑖ(2)J•77Ḅᑖâᑡ"01245810P0.390.030.170.090.110.110.10Ä(EC”)=0x0.39+1x0.03+2x0.17+4x0.09+5x0.11+8x0.11+10x0.10=3.16------10ᑖîËVgn_`ab,ᑣQᨵP(€=0,n=1)=p(\=O)P(n=DÀP(€=O,n=2)=p(€=O)P(n=2)ÀP(À=Ln=1)=P(€=1)P(n=1);P(E=1,n=2)=P(g=1)P(n=2)ÀÄ(PC=O஻=1)_º_=0õ=2)_P(g=O)=BPC="=2)—P~=1)0.050.12÷————ᦑgné_`ab஺0.030.10ø.ËVᵫᐰᭆ᳛úûüBayes
()=0.1X0.9+0.9X0.2=0.27----------------------------------5ᑖᡝ(ᩭ᳛Ḅ)=(0.1X0.9)/0.27=1/3--------------------10ᑖ#.$Ak='ᙠ)k*+,-,./᪗1,A0='4*45,./᪗1஺78P(A)=O.3;AA)=0.7X0.3=0.21;AA)=0.72X0,3=0.147Z3/,(A,)=0.7:,X0.3=0.1029;^)=0.7'=0.2401----------------------------------6ᑖᙠA5BCDEFḄᦈHgᑖJK90ᐗE80ᐗE70ᐗE60ᐗE140ᐗ஺--------------------------------------------------------------------------------------8ᑖ63

64N'OᓭᜧR(ST)UVEEC)=0.3x90+0.21x80+0.147x70+0.1029x60+0.2401x(-140)=26.65---------------------12ᑖZ.[\]F^_`ab஻defEᑣ஻22000,]ᢇef.ᔠjefᦪElmn⚗ᑖpB(n,p),p=0.95.U஻tᜧEᦑB(n,p)vwxM஻0,npq)------------4ᑖᵫᩩfᨵP>2000)x1-জJ஺\)=0.95-----------------------------------8ᑖUজ(1.65)=0.95,ᦑn=—L65,[.2123,ᓽ^_⌕ab2123def.------------------------------------------------------------12ᑖ.:UAஹBஹC,ᦑP(AC)=P(A)P(C),P(BC)=P(B)P(C),P(AB)=P(A)P(B),P(ABC)=P(A)P(B)P(C).P((AUB)C)=P(ACUBC)=P(AC)+P(BC)-P(ABC)----2ᑖ=P(A)(C)+P(B)P(C)-P(A)(8)(C)---------------------4ᑖ=[P(A)+P(B)_P(A)P(8)]P(C)=P(AUB)P(C)ᦑAUBxC.------------------------------------------------------6ᑖீᔁᓝுஹ8⚪(ᐳ7ᑖE⚪1ᑖ)1.]A,8,CKfEᑣAxAuBuC8Ḅ.2.F(x)8¢᝱¤¥Ḅᑖp¦ᦪEᑣ(§.1(x).3.¨¤¥XxYEª«¬1x1Ḅᭆ᳛ᙳK0.5,ᑣ¯=°.4.±²³´µ¶·n¸ᙳᒴᑖpḄ²ºᑖp»8ᙳᒴᑖp.5.᪵½ᙳ¾Ḅ¿ÀX28ÁÂÃÄ¿ÀḄÅÆÇÈ.6.ᙠÉÊḄËÌÍl-aDEÐÇÑᦪḄËÌÒÓÊÔ.7.ᙠÑᦪḄᎷ]Ö×.EØÙ¶Ḅµ8᪷ÛᜓÝᎷ]ÞßÊḄ.nஹ⌱Ý⚪(15ᑖE⚪3ᑖ)(1)]BuA,ᑣD☢¢ßḄ±8.(a)P(Þ)=1—P(A)â(b)äåå=P(ᔊP(N)â(c)P(5IA)=P(B)â(d)P(AI5)=P(4)(2)ëᦣí¤¥XḄᭆ᳛ᑖpK(X=k)=î=1,2,…)Ḅᐙ⌕ᩩf864

65N'OᓭᜧR(ST)(a)ñ=(1+A)”ò4>0â(b)/1=1-4ò0<ñ<1â(c)/1=D|—1òõ<1â(d)A>0òO?(-2,2)@ḄᙳᒴᑖBᑣ45=y=X?Ḅᭆ᳛EFGᦪ/y(y)=.(3)345=(X,y)~N(0,22;l,32;0),ᑣᭆ᳛P(|2X—y|Nl)=.(4)345=(X,Y)ḄὶᔠᑖBK(x,y)(1,0)(1,1)(2,0)(2,1)P0.40.2abLE(XY)=0.8ᑣcov(X,F)=.(5)3(X1,X2rX6)ᩭNO᝱ᑖBN(0,l)Ḅ᪵,36r=(£x.)2+(£x,.)2(i=li=465

66"S,TᓭᜧWXYZ[\©=^cY>?32ᑖBEXc2[=.X6[3efghij^kX~NX஻er?[Xᓫs(t^[u஻=9Ḅ᪵w᪵ᙳxᑖyᐘ=6,S?=0.33,ᑣ஻Ḅ}~F95%Ḅᓫ}~k@▲(.ஹᵨ⚪X54ᑖ2⚪9ᑖ[1.eᔆᓱ〈■“ᐺᵨ⚔10ᐸ5ᵨஹ2ᵨஹ3¡¢£¤.ᑮ¦Ḅᙢ^¨©ªᜫ19ªᜫ¬.©?ᒕ9®¯ᡭ±2²³´ᵨµªᜫḄ¶ᵨḄᭆ᳛.2.345=XX,Y[ḄὶᔠEFGᦪJA0ᔠ⚪4Aᜧ⚪ᐳ2D⚪ED⚪12ᑖᐳ24ᑖ928.GHIJKLMᦈOPQ᎛ḄSTX4ᓫ6ᑖW9Xᦪ/ᐭ=gḄᢣᦪᑖ.419\JGᙠ]ᦈOPQ᎛ST^I10ᑖWḄᭆ᳛pb66

67cᓭᜧ4ef92"gG•iᨴ⌕lI]ᦈOPmnᵨY⊤qQ᎛ST^I10ᑖWḄnᦪᑏsYḄᑖt,v\P{Y>1}.29.wxyXḄᭆ᳛z{/XfM=\2,04x42;0,ᐸ.|\6(1)E(X),D(X)b(2)D(2-3X)b(3)P{O2.0639,S/AM15/V2511µ¶gᎷw¸,-./ᐰ1ὃḄᦪᙳᡂ/70ᑖ஺<ஹ>ᔠ⚪67

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