1、BBA0B5A6 1 C8 BMAKBIAWC6B8 1B7DC1.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1A6 2 C8 BMAKDGB3AOBCB8ACDI 13B7DC2.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13A6 3 C8 AABTBMAKDGB3AOBCB8ACDI 27B7DC3.1 . . . . . . . . . . . . . . . . . .
2、 . . . . . . . . . . . . . . . . . . . 27A6 4 C8 BMAKDGB3A4BKCHBOCA 47B7DC4.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47A6 5 C8 A2BKA8B6AOCFC2AMC0A8B1 64B7DC5.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64A6 6 C8 BKB1BRAQA4AIDECDBG 71
3、B7DC6.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71A6 7 C8 A0BKAGAQ 79B7DC7.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79A6 8 C8 ASBEAUC4 90B7DC8.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90A0AZBVBY 1
4、01iii D8A1D5A7 1 C9 BNALBJAXC7AFB9BXBQ1.1(A)1. C1CTBBAVCUB3BYCXABCYB4DGBUAG(1) DIDHCBCSAD10CMA5AB6CMARA5AB4CMACA5ABBSBEBCAD1 10A2ABD4CBAHA8D4A5ABD4C2A5ABA2CBAI(2) C5AQBPDDCYABBSBED4C2D9CTBIANCBAI(3) D4AFB5APAVD3ABD4C2D9CBAPD3CBAI(4) C31 BUC7ABCPCYBJCGAVB4ABD4C2CNB4C7B2AY (1) = 1,2,3, ,10.(2) = (i,j)
5、| i,j = 1,2,3,4,5,6.(3) = 0,1,2,3.(4) = (x,y,z)|x 0,y 0,z 0,x+y +z = 1.2. CUB3AN x BHB7A7BU a,b B2BLD4BUC1ABBKD8 x|a lessorequalslant x lessorequalslant b, B8 =x| 1,DHD2 AB negationslash= .AHP(AB) = P(A) +P(B)P(AB).DHD2A2 P(AB) A8AAA5D7DCBYBJAB P(AB) A8AAD7BVBYD0A2 AB = BJAB P(AB) A8AAD7BVBY (BLCJBV
6、D4CMCRBSCBDIC1).9. B8ADN C1C4D1ABD9CBADM C1D3D1ABCID4CBAHA8nC1ABAYD9CBDFADm(m lessorequalslantM)C1D3D1ABCFBABVB7B3AJAY B8 ABDBSBUC1A6D9CBDFADmC1D3D1A7ABB2B4BUC1D2CBAGCnN. ACBAXDHB2B4BUC1CMCBAG CmMCnmNM.P(A) = CmMCnmNMCnN .10. D4C9D5DDCLCW52BG(BQADDCAIA2BVAI), COCMAFBEB1D4BGD4BGAKC8ABAYABBNC8AFCOCMAF
7、DFA0BRCMAFB0C8A5D4CFAKAXABCFBABVB7B3AJAY B8 ABDBSBUC1A6DFA0BRCMAFC8A5D4CFAKAXA7 52BGCLAB 4CMAFBEB1D4BGD4BGAKC8CWAD52!13!13!13!13!CFC8BCBRCMAFC8A5D4CFAKAXCWAD 4!CFC8BCP(A) = 4!52!13!13!13!13!= 4!(13!)452! .4 CP1 A4 DECWDCD2A3CTD711. D4 5 CEBLA3BZA2ABBZCYCBAHCK 4C2AB 4C2BZCYCBC6B3AD 2C2CUCGD4CEABCFBAB
8、VB7B3AJAY B8ABDBSBUC1A64C2BZCYCBC6B3AD2C2CUCGD4CEA7ABD45CEBLA3BZA2ABBZCYCBAHCK4C2ABBNA2AID410C2BZCYCBAHCK 4C2CWADC410CFCKBC4C2BZCYABBNBQADCUCGCEABBNA2AID4 5 CEBZCBCK 4 CEBZCYABB7BL 4 CECBABD4CEBZCBA8CTD4C2ABCWADC45 24 CFCKBCD0P(A) = C4524C410 =821, P(A) = 1P(A) =1321.12. D4ARBOB3C5ABC5A2CCB5AD25 C0C
9、HDFABABCO9CMBEABBRAUCHDFB0DCCFAKB7 9 CMBECBAHDCD4BEBBCCABC5A2CCC2B7ADCHDFBBCCBJBQA0CCABA6BBAVBUC1ABCFBAAG(1) C5A2CCB7ALiBEA0CCAI(2) C5A2CCB7ALiBEA3ALj BEC6B3ADD4BEA0CCAI(3) C5A2CCB7ALiBEA3ALj BED1A0CCAI(4) B7ALiBEAD3 AFBBCCAY B8 AiA6BDBSC5A2CCB7ALiBEA0CCA7(1)25C0CHDFBRAFB79CMCCBEABC9CMCCBEBBCCB0BVDC
10、CFABDHD2BRCMAFCWAD 9CFBBBC 25 CMAFCWAD 925 CFBBBCAL iBEBQAFBBCCABBNA2AIBRCMAFC2AD 8CFBBBC 25CMAFCWAD825 CFBBBCP(Ai) = 1P(Ai) = 1 825925 = 1(89)25.(2)P(Ai Aj) = 1P(Ai Aj)= 1P(Ai Aj)= 1 725925.(Ai Aj BDBSAL i,j AQBED1B1AFBBCCABBBBRCMAFC2AD 7 CFBBBCAB 25 CMAFCWAD 725CFBBBC)(3)P(AiAj) = 1P(AiAj)= 1P(Ai
11、Aj)DJDG1.1 5= 1P(Ai)P(Aj) +P(Ai Aj)= 1(89)25 (89)25 + (79)25= 12(89)25 + (79)25.(4)ALiBEADD9AWABAVCMAFBBCCABCWAD822 CFBBBC(BFBBAB22CMAFABBRCMAFAD8CFBBBC).DHD2AL iBEAD 3 CMAFBBCCABCWAD C325 822 CFBBBCCZD9AL iBEAD 3 CMAFBBCCABCFBAAOC325 822925 .13. AHA8AQCMBLDCAI 1ABBQCBABA6D1BTABB5BLDCAI29 , A1D1BTAB
12、A3BLDCAI1ABCFBAAY B8AQCMCBBSBEAOx,y,A BDBSBUC1A6AQCBBWA3BLDCAI 1, D1BTBWB5BLDCAI29 A7ABBB = (x,y)|0 0,0 k.AAD7BVADPX klessorequalslant 5%. BBPX lessorequalslant kgreaterorequalslant 0.95. AAAIC010 (0.92)10 +C110 (0.92)9 0.08 = 0.4344+ 0.3777 1.DJDG2.1 17AY AAintegraldisplay +f(x)dx = 1ADintegraldisp
13、lay +0ke3xdx = 1,CDAAk = 3.Px 1 =integraldisplay +1f(x)dx =integraldisplay +13e3xdx = e3.17. D7BVCUB3BBAS X ABBSBMDICBAOF(x) =0, x 0,BYA6AG(1) C6CB AA3B;(2) CFBABVB2f(x);(3) X BHB7A7BU(1,2) CDABCFBAAY (1)CPCYBSBMDICBABAGAMCJCBABADlimx0+F(x) = A +B = F(0) = 0,AHlimx+F(x) = 1,BBA = 1.D4B9A = 1,D0B = 1
14、.(2)f(x) = F(x) =xex22 , x 0,0, xlessorequalslant 0.(3)P1 3 =integraldisplay +3f(x)dx =integraldisplay 5313dx =23.AZ A BDBSBUC1A6B6X B1AID4C2 3 D3ABC6B3AD2 D3D4C2BYDCAI3 A7ABBBP(A) = C23(23)2 13 +C33(23)3 = 2027.21. B8CUB3BBAS X ABCFBABVB2AOf(x) =braceleftBigg2x, 0 100,0, xlessorequalslant 100,BYA6A
15、G(1) BOA8C3C1B7150BVBJD9B2ABCFBAAI(2) 3C2CDC7A2ABAPCYD5BOA8AT 150BVBJB0BLCWAQABCFBAAI(3) 3C2CDC7A2ABAPCYD5BOA8AT 150BVBJC6B3ADD4CMBLCWAQABCFBAAY (1)PX 150 =integraldisplay +150100x2 dx =23.(2)3C2CDC7A2ABAPCYD5BOA8AT 150B0BLCWAQABCFBAAO(23)3 = 827.(3)P = 1(1 23)3 = 1 133 = 2627.23. B8D1DFA5C5DJCACYDI
16、DIC6B3ABBJBU X( DJAUAG min) C6D4BZCBBSBMABD9BVB2DICBAOf(x) =15 ex5 , xgreaterorequalslant 0,0, x 10 =integraldisplay +1015ex5 dx = e2,PY = k = Ck5e2k(1e2)5k (k = 0,1,2,3,4,5).PY greaterorequalslant 1 = 1PY 150 = 1PX lessorequalslant 150= 1PX 20018 lessorequalslant 15020018 = 1(5018) = (259 ) = 0.997
17、3AAAI0.9973 99%,D0A6AGD0A625. CICLBWAOCLD7BYABCBCLCGB6CLCQAKC6D4BQD5BSBM N(65,102). ANDD85BSD9B2AOA9CEABAYCBCLCGB6AOA9CEABD7BBDCC7BDD2AFCBABASBSBWBDAJAY A8X BDBSC5CMCLBBAOCLD7BYABCBCLCGB6ABPX 85 = 1PX lessorequalslant 85 1(856510 )= 1(2) = 10.9772 = 0.0228.A9CEABD7BBDCC7BDD2CBAB2.28%.26. B8CUB3BBASX
18、 C6D40,5B2ABD1B2BSBMABA6BJCI4x2 +4Xx+X +2 = 0ADBNCPABCFBAAY AAAIX B70,5 B2C6D4D1B2BSBMABBBPX 2 = P2 2;(4) PX 3.AY (1)P2 2 = PX 2+PX 3 = 1PX lessorequalslant 3 = 1(332 ) = 1(0) = 0.5.28. D7BVCUB3BBAS X ABCFBABSBMAOX 2 1 0 1 2 3P 0.1 0.2 0.25 0.2 0.15 0.1A6AG(1) Y1 = 2X ABBSBMAVAI(2) Y2 = X2 ABBSBMAV2
19、2 CP2 A4 DECWCKD4CYD9CTD7CSCLAY (1)Y1 -6 -4 -2 0 2 4P 0.1 0.15 0.2 0.25 0.2 0.1(2)Y2 0 1 4 9P 0.25 0.4 0.25 0.129. B8CUB3BBAS X ABBVB2DICBAOf(x) =1pi(1 +x2) , x greaterorequalslant 0,0, x 0).limx+ex = + limxex = 0.BBY ABCFBABVB2fY (y) =fX(lny)|1y|, 0 0,0, y lessorequalslant 0.31. B8CUB3BBAS X C6D4BT
20、CBAO12 ABBZCBBSBMABBTBYAGY = 1e2XC6D40,1 B2ABD1B2BSBMAY AAAIX C6D4BTCBAO12 ABBZCBBSBMABD0D9CFBABVB2AOfX(x) =braceleftBigg2e2x, x 0,0, x lessorequalslant 0.AAAIy = 1e2x CWCWDCA3A1CQCLDJATlimx(1e2x) = limx+(1e2x) = 1,BBY ABCFBABVB2fY (y) =12fX(12 ln(1y)11y, y 0 BJFW(w) = PI2 lessorequalslant w2 = PI l
21、essorequalslantradicalbiggw2= FX(radicalbiggw2 ).D0FW(w) =1, w 240 = 1(45) = 0.2119.(1)P(B) =2summationdisplayi=0P(Ai)P(B|Ai)= 0.10.2119+ 0.0010.5762+ 0.20.2119= 0.06415.(2) = PA1|B = P(A1)P(B|A1)P(B)= 0.0010.57620.06415 = 0.00898.3. B8AXCQB5B1C5C7BCABD3BRCYC3 X N(0,202)(DJAUAG m), BYA6AG(1) B5B1D4A
22、1ABD3BRCYC3D0B6BYCBDE20mABCFBAAI(2) B5B13A1C6B3AD1A1ABD3BRCYC3D0B6BYBLCBDE10mABCFBAAY (1)P|X| 20 = 1P20lessorequalslant X lessorequalslant 20= 1P1lessorequalslant X 020 lessorequalslant 126 CP2 A4 DECWCKD4CYD9CTD7CSCL= 1(1)(1)= 2(1(1) = 0.3174.(2)P10 19.6 = 10.95 =0.05,BBB7100 D3B1AIBZASCBC6B3AD3 D3
23、BZASB4C3D0B6BYDCAI19.6ABCFBAAO12summationdisplayk=0Ck100(0.05)k(0.95)100k 12summationdisplayk=05ke5k! = 0.87(AABKCRAWAC).5. D4BND2B3CWAD300D4BSB3ABD2B3AD13DICBBLBLABBQB8BRD4BSB3BRD2B3D0CBBLBLABCFBAAO 3%, A6BRD4BSB3BRD2B3D0CBBLBLBJABCFBABJAAA5BMD4ABCFBAA3A3BJBRD2B3D0CBBLBLABBSB3ABD7DCCFD4CBAY A8X BDB
24、SC5D4BJDEBSB3BRD2B3D0CBBLBLABD4CBABBBBRD4BSB3D0CBBLBLBJCFAAA5BMD4ABCFBAAOPX lessorequalslant 13 =13summationdisplayk=0Ck300(3%)k(97%)300k13summationdisplayk=09ke9k! = 0.9265(AABKCRAWAC).AAAI(300 + 1)3% = 9.03 = 9 A1 (300 + 1)3% BLBVBPCBD0A3BJBRD2B3D0CBBLBLABD7B7D4CBAO9 D4A7 3 C9 ABBUBNALDHB4APBDAFB9
25、ADDJBXBQ3.1(A)1. A3D4D1CFAB 5CMC4D1CBABAD 2 CMBQD1BRD3D4CBCKD4CMBWCXCAASABBLBMAUAKAMCJCSA82 D3BKA6Xk = 0 A7BDBSALk D3A8A5BQD1ABB9A6Xk = 1 A7AOALkD3A8A5D3D1 (k = 1,2). C1CT (X1,X2)ABALA6BSBMB9AY P = X1 = 1,X2 = 0 =35 24, PX1 = 0,X2 = 1 =25 34.PX1 = 0,X2 = 0 = 25 14, PX1 = 1,X2 = 1 = 35 24.D0(X1,X2)AB
26、ALA6BSBMB9AOa72a72a72a72a72a72a72X1X2 0 10 110 3101 310 3102. D4DIDHCBCSAD4CMA5ABD5D3BCAD1,2,2,3. CID4DIDHCBAHA8 1 A5ABA8BLBMAUABB6D4DIDHCBAHA81 A5D9 X A3Y BSBEBKALD4D3A2ALBAD3A8AAABA5B2BCADABCBD0ABA6AG(1) (X,Y )ABCFBABSBMAI(2) PX +Y greaterorequalslant 4.AYa72a72a72a72a72a72a72XY 1 2 31 0 16 1122 1
27、6 16 163 112 16 028 CP3 A4 CRDIDECWCKD4CYD9CTD7CSCLPX = 1,Y = 1 = 14 0 = 0, PX = 2,Y = 1 = 14 23.PX = 3,Y = 1 = 14 13, PX = 1,Y = 2 = 24 13.PX = 2,Y = 2 = 24 13, PX = 3,Y = 2 = 24 13.PX = 1,Y = 3 = 14 13, PX = 2,Y = 3 = 14 23.PX = 3,Y = 3 = 0.3. B8DIDHCBAD 5 CMA5ABBSBEBCADA2BI 1,2,3,4,5, BID4BLDIDHC
28、BAHA8 3 CMA5ABX,Y BSBEBDBSA8CTABA5ABD7DCBCA2A3D7BVBCA2A6BAAPCUB3BBAS (X,Y)ABCFBABSBMBAB8AYCFBABSBMAY PX = 1,Y = 3 =1C35 =110,PX = 1,Y = 4 =C12C35 =15,PX = 1,Y = 5 = C13C35 =310 .a72a72a72a72a72a72a72XY 1 2 33 110 0 04 15 110 05 310 210 1104. C3D4BPA7B7AMC5 3 D3ABD9 X BDBSB7 3 D3CBCTBIBQBWABD3CBABD9 Y BDBSB73 D3CBCTBIBQBWD3CBALBGBWD3CBBWC3ABD0B6BYABBYA6AG(1) (X,Y )ABCFBABSBMAI(2) D3AIX,Y ABB8AYCFBABSBM
