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Đề thi kết thúc học phần học kỳ II năm học 2017-2018 môn Thống kê nhiều chiều giúp các bạn sinh viên có thêm tài liệu để củng cố các kiến thức, ôn tập kiểm tra, thi cuối kỳ. Đây là tài liệu bổ ích để các em ôn luyện và kiểm tra kiến thức tốt, chuẩn bị cho kì thi học kì. Mời các em và các quý thầy cô giáo bộ môn tham khảo.
0,00KH04,yo TRU'ONG DAI HOC KHOA HOC TIf NHIEN, DHQG-HCM MA LLIU TRU DE THI KkT THOC HQC PH AN H9c kST II — Nam h9c 2017-2018 (do ph)ng KT-DBCL ghi) LP/R TI-126 Ten h9c phan: Themg Ke Nhi6u Chi6u Ma" HP: TT H 2,01 Thbi gian 1àm bai: 90 phirt Ngay thi /1/ 06/ IOW Chi chit: Sinh vier/ dttoc phép 10 kitting dttvc phepl si2 dung tai 1iv lam bai Ghi chü them: SV ducic pile') sir dung mOt td giAy A4 chuAn bi (vi6t tay, có ghi MSSV, h9 ten) va Op kern bai thi Bai (2 digm) X1 (ill all 0- 12 0-13 C110 X rs-' A.r3(tt, E) v6i X = (X2) ; tt = /22) vil E = (012 022 023 X3 V13 013 023 033 Tim phan ph6i cfra, ( voi Yu = X1 — X2 IA Y2 = X2 — X3 I Bai (2 dim) Cho X ,, J\/;,(//,, E) (tan OA ma trhn nghich dao E-1) X = (x X12 ) = (pi); E (Ell E12) P.2 E21 E22 voi X1 la, vector Ap (q x 1), X2 lh vector CAP ((p — q) x ); PI E tz2 E Tim ham mat di, dieu kien cfra, X1 bit X2 = x2 BM (3 diem) Nhung quan trgc tren hai Wen dap ling throe thu thap cho ba lieu phap (three treatments), cac vecto quan trgc (T1) : X2 - lieu phap 1: (6) ( 5\ (`° (4 ) ( 7 ' 9/ Of 9 9 ' - lieu phap 2: (33 ), (612), ( 3), - lieu phap 3: (32), (50 , (0 , (32 ) a Xay dog bang MANOVA cho so sanh cac vecto trung binh trig the' dva tren mO hinh )(LI = 11, eij vOi = 1,2, va j = 1,2, , n1 Trong cac eti dc lap cling phan phi 1V;)(0, E): it lh trung binh chung; r la anh hrtang cila, lieu phap alit volt E ncri b Da \Tao bang sau, thilc hien kiem dinh cho nhfing anh hirang cUa cac lieu phap voi mix ST nghia a = bit rang T44),V = 4,77 De thi Om trang) 1 1/3] 4),zr ,ocKH04, TRVONG DAI HOC KHOA HOC TV NHIEN, DHQG-HCM MA LU'U TRO' e 0, DE THI KkT THUC HOC PI-1.7^iN iN Hoc IcS7 II - Nam hoc 2017-2018 Table 6.3 Distribution of Wilks' Lambda, A* = wl/ls + C (dr, phemq KT-DBCL )ht,) No of No of variables groups Sampling distribution for multivariate normal data p 1 g p = 2 g pl g=2 g ( Int, g F8-1.int-s 1 A* 1) (1 - VA+ ) g - 1 VA,-; ( Inc - g ()-n t, - -11) ( - A*) A* (Inc - p - 2) /1_ \/A* \IA* FP Ent-P-1 F2p,2(1.nr -p- 2) Bai (3 diem) lieu ducic thu thap qua cuPc khao sat ye quST theii gian (danh cho cac hog, dPng khac ngay) cüa mPt ngi Ta quail tarn den 10 bin dinh ltrong (tlaoi gian (dv: gi6/100) danh cho 10 hog Ong khac 24 gi6) cUa 28 liguei: PROF (nghe nghiep), TRAN (di lai), MENA (dpn dep nha, cfra), ENFA (con cal), COUR (di chp), TOIL (ve sinh ca, nha,n), REPA (an u6ng), SOIVIM (ngu), TELE (xem TV), LOIS (the; thao, giai tri) Chung ta tin hanh phan tich phan el-1111h (PCA) tren dti lieu sau dã chuA,n hoa 10 bien Voi cac ket qua, nhan dime (nho phan mem R) dtrdi day, ta nen giff 14i raw phan chit-1h? VI sao? 'At ke cac phan chInh (Noe chpn? Cac bin nao gop phan iOn xay ding nen hai phan el-1Mb dau tien? giti thich (thong qua h s6 Wong quan )? comp comp comp comp comp comp comp comp comp comp 10 eigenvalue percentage of variance cumulative percentage of variance 4.588669e+00 4.588669e+01 45.88669 2.119843e+00 2.119843e+01 67.08511 1.320978e+00 1.320978e+01 80.29490 1.195255e+00 1.195255e+01 92.24745 4.684105e-01 4.684105e+00 96.93155 1.990474e-01 1.990474e+00 98.92203 4.681319e-02 4.681319e-01 99.39016 3.706510e-02 3.706510e-01 99.76081 2.391893e-02 2.391893e-01 100.00000 1.494514e-32 1.494514e-31 100.00000 Standard deviations: [1] 2.142118e+00 1.455968e+00 1.149338e+00 1.093277e+00 6.844052e-01 4.461473e-01 [7] 2.163636e-01 1.925230e-01 1.546575e-01 1.124319e-16 Rotation: PC1 PC2 PC3 PROF -0.45617162 0.08313782 0.073587007 PC4 PC5 PC6 TRAN -0.45738827 -0.03991548 0.007303258 0.06123280 -0.140328264 0.04064934 0.04166767 0.162269266 -0.01895219 MENA 0.42009993 -0.01555795 -0.315341555 ENFA 0.40712005 -0.12264860 -0.072851719 0.96932467 0.277549704 0.19589470 -0.006074950 -0.09766395 0.57174504 thi g6ni trang) [Trang 2/3] TRU'oNG DAI HOC KHOA HOC Tlf NHIEN, DHQG-HCM MA Lilt." TRU ( loft V IPHOCPIUMIHO COUR TOIL REPA SOMM TELE LOIS PROF TRAN MENA ENFA COUR TOIL REPA SOMM TELE LOIS 1FITI KET THUC IIQC PHAN Hoc kir II - Nara hoc 2017-2018 feb 1)111,11 ,1 KT-1)13CL 0.26310001 -0.52241218 0.003967461 -0.11071136 0.124557933 -0.61031345 0.03711770 -0.56189036 0.262902171 -0.05812977 -0.655263317 0.36246486 0.27465298 0.45973933 0.370916117 0.01293150 -0.003644108 0.11412606 0.30072032 0.39101336 0.166054341 -0.28583091 -0.457422601 -0.24393929 0.04642008 -0.13262215 0.809201165 0.13834203 0.351950788 -0.09820510 0.04303032 -0.07572669 -0.026292895 -0.87576408 0.314488720 0.27480748 PC7 PC8 PC9 PC10 -0.06675463 0.489097798 -0.09531879 0.70832772 0.30461479 -0.420263064 0.68469116 0.15003163 -0.06475390 -0.513338595 -0.15232809 0.62045982 0.36483611 0.369269960 0.24275152 0.09511692 -0.12200791 0.337151011 0.34452689 0.10167821 -0.10567047 -0.168510499 0.09379873 0.03597011 -0.59004121 0.002283305 0.45589656 0.08016202 0.59344728 0.080942595 0.10625604 0.09294598 0.19317992 -0.174400503 -0.29986126 0.12307359 -0.04190751 -0.072432310 -0.05860395 0.19975088 HAT (De thi gnit trang) [Trang 3/31 K HO4 Rtfd N G Ma ji DAI HOC KHOA HOC TI.1NHIEN, DHQG-HCM DE THI KE1"11HUC HOC PHAN Hoc kr II — Nam hoc 2017-2018 MA LUIJ TR.tf(do phong KT-DBCL 9hi) b) Ngttdi trA, Idi din thoai chi an nao du 15 cu6c gi thi moi di an trim Tinh kI \wig thdi gian cho cüa ngtrdi c) Bit rang co k cu6c goi an trong bon giO du tiën TInh xac suk de' co j-cu6c gcoi d6n mOt gid du tien (j < k) Cau (2.0 diem) Mt dm hang nho c6 ngudi phvc vv dOc lap va thdi gian phvc vv cüa m8i ngudi Co phan ph6i mu v6i k57 \Tong la 1/2 gid SO khach an cda hang c6 phan phoi Poisson vdi ti 1-e ngudi mOt gid Gia sir them rang cit'a hang chi c6 th phvc vv toi da ngutii a) Tinh va giai thief' 1.6 rang ti le khach an (ti sinh) tir) µi va, ti le khach dude ptive vv (ti so khach trung binh cira hang sau Wit thdi gian dai phvc vv c) Tinh ti I khach hang ti6m nang an ca hang b) Tinh Cali (2.0 diem) Cho X(t) va, Y(t) la hai qua trinh Brown chuAn dOc lap Ardi a) CI-rang minh rang Z(t) = X(t) — Y(t) ding la, qua, trinh Brown b) Tim phtrong sai cüa Z(t) A thi gOIT1 trang) [Trang 2/2] (H04 ,, TRU'ONG DAI HOC KHOA HOC NHIEN, DHQG-HCIVI MA LU'U TRU (do plOng KT-DBCL yhi) DE THI KET THUC HOC PHAN Hoc kST II — Nam hoc 2017-2018 C,741/2_171-10 Ten h9c phan: Toan Ting Dung va Thong Ke Ma HP: Ti H Ngay thi ,(0/06/ ZO/W ThOi gian lam bai: 90 phut Chi chit: Sin,h, vien ID duct phep / N khong duo'c phepi sz't dung tai lieu lam bai Ghi chit them: SV ditoc phep sit dung mOt to giAy A4 chuL bi sn (vi6t tay, có ghi MSSV, 119 ten) va, Op kern thi BM (1,5 dim) Wit tram chi phat hai loai tin hieu A va, B vOi xac suAt Wong itng 0,84 ye, 0,16 Do có nhi6'u tren cluOng truAn nen 1/6 tin hieu A bi lech va dtroc thu nhlr tin hieu B, 1/8 tin hieu B bi lech tin hieu A a Tinh xac suAt thu dttoc tin hieu A b Giasi thu &roc tin hieu A, tim xac sugt d thu diroc dung tin hieu 1c pita Bai (2,5 die'rn) Cho vecto ngAu nhien (X, Y) có bang phan phi xac sut sau: 3c 2c c c 4c 2c 2c 5c a Hay xac dinhhng s6 c, sau tim cac ham mat dO1 (phan ph6i xac suit bien) f x (x) fy(y) b Tinh fxiy=y• Bai (4 dim) Mt bai bac) tap chi Journal of Sound and Vibration (Vol 151, 1991, pp 383-394) mo fa mOt nghien citu v m6i quan h gifia s phoi nhi8m tigng 8n va, viec tang huy6't a Dir 1iu sau di/0c lgy di din ti chi lieu dttoc trinh bay bai bao 1 x 60 63 65 70 70 70 80 90 80 80 85 89 90 90 90 90 94 100 100 100 a Ve d8 thi phan tan cna y (huy6t áp tinh Wang milimet thity ngan) theo x (cueng clO am tinh bng decibels) MO hinh hi quy don có phil hop trtrang hop nay? b Ve &rang thing h8i quy tren ding he' truc toa dO ô cau (a) Cho to'ng binh phtfong sai s6 SSE = 31,266, tim ttoc ltrong cna, o-2 (Lroc Wong cho pinking sai caa sai s6 m6 hinh hOi quy don tren) c Tim mile huy6t áp trung binh Wong ling NT& ctrOng di) am tha.nli 85 decibels Tim khoang tin cy 95% cho in& huytt áp trung binh d MOt ngtroi cho eang phoi nhi8m titng n va tang huy6t Ai) khOng Wong quan vOi Hay kie'm dinh thuyet tren vói mire Sr nghia 5% A thi g -trang) rang 1/4) ,koCKHo e TRUONG DAI HOC KHOA HOC TI,J NHIEN, DHQG-HCM MA LU'U TR 0° g 115N Hoenimi DE THI KkT THUC HOC PHAN Hoc kST II — Nam hoc 2017-2018 (do pluing K7'-D13CL ght,) Bai (2 diem) Ta xet mo hinh hOi quy b6i sau: Y =/30 + 01 x1 + 029:2 ± E a Hohn thhnh bang ANOVA sau: NguOn g6c bi6n dOi I-16i quy Sai s6 TOng quat TO'ng binh *song b-ac tis Trung binh binh phisong Th6ng ke F, 532,3 147889 b Kiem dinh giii thi6t 110 : /31 = 02 = Voi mile Y nghia 5% HT ten ngt1oi de/MSCB: Nst.itAp Thi T.g9c Hp ten ngd6i duyet de Hp Chit kSr Chit ky• (De thi gin trang) [Trang 2/4] g tv 136.ng A.4: Phan vi t cüa phan phi Student 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 40 60 120 0.60 0.75 0.90 0.95 0.975 0.99 0.995 0.9995 0.3249 0.2887 0.2767 0.2707 0.2672 0.2648 0.2632 0.2619 0.2610 0.2602 0.2596 0.2590 0.2586 0.2582 0.2579 0.2576 0.2573 0.2571 0.2569 0.2567 0.2566 0.2564 0.2563 0.2562 0.2561 0.2560 0.2559 0.2558 0.2557 0.2556 0.2550 0.2545 0.2539 1.0000 0.8165 0.7649 0.7407 0.7267 0.7176 0.7111 0.7064 0.7027 0.6998 0.6974 0.6955 0.6938 0.6924 0.6912 0.6901 0.6892 0.6884 0.6876 0.6870 0.6864 0.6858 0.6853 0.6848 0.6844 0.6840 0.6837 0.6834 0.6830 0.6828 0.6807 0.6786 0.6765 3.0777 1.8856 1.6377 1.5332 1.4759 1.4398 1.4149 1.3968 1.3830 1.3722 1.3634 1.3562 1.3502 1.3450 1.3406 1.3368 1.3334 1.3304 1.3277 1.3253 1.3232 1.3212 1.3195 1.3178 1.3163 1.3150 1.3137 1.3125 1.3114 1.3104 1.3031 1.2958 1.2886 6.3138 2.9200 2.3534 2.1318 2.0150 1.9432 1.8946 1.8595 1.8331 1.8125 1.7959 1.7823 1.7709 1.7613 1.7531 1.7459 1.7396 1.7341 1.7291 1.7247 1.7207 1.7171 1.7139 1.7109 1.7081 1.7056 1.7033 1.7011 1.6991 1.6973 1.6839 1.6706 1.6577 12.7062 4.3027 3.1824 2.7764 2.5706 2.4469 2.3646 2.3060 2.2622 2.2281 2.2010 2.1788 2.1604 2.1448 2.1314 2.1199 2.1098 2.1009 2.0930 2.0860 2.0796 2.0739 2.0687 2.0639 2.0595 2.0555 2.0518 2.0484 2.0452 2.0423 2.0211 2.0003 1.9799 31.8205 6.9646 4.5407 3.7469 3.3649 3.1427 2.9980 2.8965 2.8214 2.7638 2.7181 2.6810 2.6503 2.6245 2.6025 2.5835 2.5669 2.5524 2.5395 2.5280 2.5176 2.5083 2.4999 2.4922 2.4851 2.4786 2.4727 2.4671 2.4620 2.4573 2.4233 2.3901 2.3578 63.6567 9.9248 5.8409 4.6041 4.0321 3.7074 3.4995 3.3554 3.2498 3.1693 3.1058 3.0545 3.0123 2.9768 2.9467 2.9208 2.8982 2.8784 2.8609 2.8453 2.8314 2.8188 2.8073 2.7969 2.7874 2.7787 2.7707 2.7633 2.7564 2.7500 2.7045 2.6603 2.6174 636.6192 31.5991 12.9240 8.6103 6.8688 5.9588 5.4079 5.0413 4.7809 4.5869 4.4370 4.3178 4.2208 4.1405 4.0728 4.0150 3.9651 3.9216 3.8834 3.8495 3.8193 3.7921 3.7676 3.7454 3.7251 3.7066 3.6896 3.6739 3.6594 3.6460 3.5510 3.4602 3.3735 TABLE A.3 F Distribution: Critical Values of F (5% significance level) 10 12 14 16 18 20 vi V2 161.45 199.50 215.71 224.58 230.16 233.99 236.77 238.88 240.54 241.88 243.91 245.36 246.46 247.32 248.01 18.51 19.00 19.16 19.25 19.30 19.33 19.35 19.37 19.38 19.40 19.41 19.42 19.43 19.44 19.45 9.12 9.01 8.94 8.89 8.85 8.81 8.79 8.74 8.71 8.69 8.67 8.66 10.13 9.55 9.28 5.80 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 6.00 5.96 5.91 5.87 5.84 5.82 4.56 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.77 4.74 4.68 4.64 4.60 4.58 10 5.99 5.59 5.32 5.12 4.96 5.14 4.74 4.46 4.26 4.10 4.76 4.35 4.07 3.86 3.71 4.53 4.12 3.84 3.63 3.48 4.39 3.97 3.69 3.48 3.33 4.28 3.87 3.58 3.37 3.22 4.21 3.79 3.50 3.29 3.14 4.15 3.73 3.44 3.23 3.07 4.10 3.68 3.39 3.18 3.02 4.06 3.64 3.35 3.14 2.98 4.00 3.57 3.28 3.07 2.91 3.96 3.53 3.24 3.03 2.86 3.92 3.49 3.20 2.99 2.83 3.90 3.47 3.17 2.96 2.80 3.87 3.44 3.15 2.94 2.77 11 12 13 14 15 4.84 4.75 4.67 4.60 4.54 3.98 3.89 3.81 3.74 3.68 3.59 3.49 3.41 3.34 3.29 3.36 3.26 3.18 3.11 3.06 3.20 3.11 3.03 2.96 2.90 3.09 3.00 2.92 2.85 2.79 3.01 2.91 2.83 2.76 2.71 2.95 2.85 2.77 2.70 2.64 2.90 2.80 2.71 2.65 2.59 2.85 2.75 2.67 2.60 2.54 2.79 2.69 2.60 2.53 2.48 2.74 2.64 2.55 2.48 2.42 2.70 2.60 2.51 2.44 2.38 2.67 2.57 2.48 2.41 2.35 2.65 2.54 2.46 2.39 2.33 16 17 18 19 20 4.49 4.45 4.41 4.38 4.35 3.63 3.59 3.55 3.52 3.49 3.24 3.20 3.16 3.13 3.10 3.01 2.96 2.93 2.90 2.87 2.85 2.81 2.77 2.74 2.71 2.74 2.70 2.66 2.63 2.60 2.66 2.61 2.58 2.54 2.51 2.59 2.55 2.51 2.48 2.45 2.54 2.49 2.46 2.42 2.39 2.49 2.45 2.41 2.38 2.35 2.42 2.38 2.34 2.31 2.28 2.37 2.33 2.29 2.26 2.22 2.33 2.29 2.25 2.21 2.18 2.30 2.26 2.22 2.18 2.15 2.28 2.23 2.19 2.16 2.12 21 22 23 24 25 4.32 4.30 4.28 4.26 4.24 3.47 3.44 3.42 3.40 3.39 3.07 3.05 3.03 3.01 2.99 2.84 2.82 2.80 2.78 2.76 2.68 2.66 2.64 2.62 2.60 2.57 2.55 2.53 2.51 2.49 2.49 2.46 2.44 2.42 2.40 2.42 2.40 2.37 2.36 2.34 2.37 2.34 2.32 2.30 2.28 2.32 2.30 2.27 2.25 2.24 2.25 2.23 2.20 2.18 2.16 2.20 2.17 2.15 2.13 2.11 2.16 2.13 2.11 2.09 2.07 2.12 2.10 2.08 2.05 2.04 2.10 2.07 2.05 2.03 2.01 26 27 28 29 30 4.22 4.21 4.20 4.18 4.17 3.37 3.35 3.34 3.33 3.32 2.98 2.96 2.95 2.93 2.92 2.74 2.73 2.71 2.70 2.69 2.59 2.57 2.56 2.55 2.53 2.47 2.46 2.45 2.43 2.42 2.39 2.37 2.36 2.35 2.33 2.32 2.31 2.29 2.28 2.27 2.27 2.25 2.24 2.22 2.21 2.22 2.20 2.19 2.18 2.16 2.15 2.13 2.12 2.10 2.09 2.09 2.08 2.06 2.05 2.04 2.05 2.04 2.02 2.01 1.99 2.02 2.00 1.99 1.97 1.96 1.99 1.97 1.96 1.94 1.93 35 40 50 60 70 4.12 4.08 4.03 4.00 3.98 3.27 3.23 3.18 3.15 3.13 2.87 2.84 2.79 2.76 2.74 2.64 2.61 2.56 2.53 2.50 2.49 2.45 2.40 2.37 2.35 2.37 2.34 2.29 2.25 2.23 2.29 2.25 2.20 2.17 2.14 2.22 2.18 2.13 2.10 2.07 2.16 2.12 2.07 2.04 2.02 2.11 2.08 2.03 1.99 1.97 2.04 2.00 1.95 1.92 1.89 1.99 1.95 1.89 1.86 1.84 1.94 1.90 1.85 1.82 1.79 1.91 1.87 1.81 1.78 1.75 1.88 1.84 1.78 1.75 1.72 80 90 100 120 150 3.96 3.95 3.94 3.92 3.90 3.11 3.10 3.09 3.07 3.06 2.72 2.71 2.70 2.68 2.66 2.49 2.47 2.46 2.45 2.43 2.33 2.32 2.31 2.29 2.27 2.21 2.20 2.19 2.18 2.16 2.13 2.11 2.10 2.09 2.07 2.06 2.04 2.03 2.02 2.00 2.00 1.99 1.97 1.96 1.94 1.95 1.94 1.93 1.91 1.89 1.88 1.86 1.85 1.83 1.82 1.82 1.80 I 79 1.78 1.76 1,77 1.76 I 75 1.73 71 1.73 1.72 1.71 1.69 1.67 1.70 1.69 1.68 1.66 1.64 200 250 300 400 500 3.89 3.88 3.87 3.86 3.86 3.04 3.03 3.03 3.02 3.01 2.65 2.64 2.63 2.63 2.62 2.42 2.41 2.40 2.39 2.39 2.26 2.25 2.24 2.24 2.23 2.14 2.13 2.13 2.12 2.12 2.06 2.05 2.04 2.03 2.03 1.98 1.98 1.97 1.96 1.96 1.93 1.92 1.91 1.90 1.90 1.88 1.87 1.86 1.85 1.85 1.80 1.79 1.78 1.78 1.77 1.74 1.73 1.72 1.72 1.71 1.69 1.68 1.68 1.67 1.66 1.66 1.65 1.64 1.63 1.62 1.62 1.61 1.61 1.60 1.59 600 750 1000 3.86 3.85 3.85 3.01 3.01 3.00 2.62 2.62 2.61 2.39 2.38 2.38 2.23 2.23 2.22 2.11 2.11 2.11 2.02 2.02 2.02 1.95 1.95 1.95 1.90 1.89 1.89 1.85 1.84 1.84 1.77 1.77 1.76 1.71 1.70 1.70 1.66 1.66 1.65 1.62 1.62 1.61 1.59 1.58 1.58 ‘oc O TRU'ONG DAI HOC KHOA HOC NHIEN, DHQG-HCM *ft (do IJE THI KkT THUG HOC PHAN Hoc lcST II - Nam hoc 2017-2018 Ten hoc phan.: LST thuy6t xac bai: 90 pinit Th6i gian suAt cd ban MA LU'U TRU phony KT-DBCL gin) C.0;11.t MTH M T.16 Ma HP: MTH10516 NOy thi• /6(/ Z•01 Ghi chit Sinh vien I CI duck phep / khOng duck phepj st't dung tai lieu lam bai Ma d6: 326 Nhorn BT: MSSV Ho ten • Dt; thi có 28 cau hOi, co kern theo bang tra cu6i d • Voi m6i cau h6i, chi có dap an dimg nhAt S dung but chi to kin dap an dttoc ch9n Bang tra 1Cii: đCD@PED 17.đđâPg 25.đđâgđ 1.đđââđ 3.đđââ 11.đđââđ 19.đđââđ 27.đđââđ 7.đ@ââđ 15.đđââđ 23.đđââđ 8.đâCDC) 31.đđâCDCD 16.đđOgg 2-1-đđâgg 32.đđââđ Ten cards from a deck ofplaying cards are in a box: two diamonds, three spades, and five hearts Two cards are randomly selected without replacement Calculate the variance of the number of diamonds selected, given that no spade is selected 1110.24 00.41 E 0.28 [1] 0.32 IN 0.34 The number of tornadoes in a given year follows a Poisson distribution with mean Calculate the variance of the number of tornadoes in a year given that at least one tornado occurs El 1.73 1.63 E 3.00 2.66 3.16 n n n A delivery service owns two cars that consume 15 and 30 miles per gallon Fuel costs per gallon On any given business day, each car travels a number of miles that is independent of the other and is normally distributed with mean 25 miles and standard deviation miles Calculate the probability that on any given business day, the total fuel cost to the delivery service will be less than 0.47 EJ 0.29 EI 0.23 El 0.13 I: 0.38 (De thi g6nA trang) [Trang x,oc KH0, 6, I c)(‘ TREONG DAI HOC KHOA HOC DHQG-HCM MA LU'U TRU' DE THIKETTHUCHOCPHAN HQC lcST II — Nam h9c 2017-2018 (do phOng KT-DBCI, ghti) The joint probability density for X and Y is f(x, = 0e-(x+21), x> 0, y > otherwise Calculate the variance of Y given that X > and Y > 11] 3.50 El 0.50 [1] Loo 111 3.25 EJ 0.25 A policyholder has probability 0.7 of having no claims, 0.2 of having exactly one claim, and 0.1 of having exactly two claims Claim amounts are uniformly distributed on the interval [0, 60] and are independent The insurer covers 100% of each claim Calculate the probability that the total benefit paid to the policyholder is 48 or less 11 0.924 El 0.320 E 0.800 0.400 EI 0.892 Automobile policies are separated into two groups: low-risk and high-risk Actuary Rahul examines low-risk policies, continuing until a policy with a claim is found and then stopping Actuary Toby follows the same procedure with high-risk policies Each low-risk policy has a 10% probability of having a claim Each high-risk policy has a 20% probability of having a claim The claim statuses of polices are mutually independent Calculate the probability that Actuary Rahul examines fewer policies than Actuary Toby E 0.3571 110.3214 El 0.2857 [j] 0.4000 E 0.3333 A company offers a basic life insurance policy to its employees, as well as a supplemental life insurance policy To purchase the supplemental policy, an employee must first purchase the basic policy Let X denote the proportion of employees who purchase the basic policy, and Y the proportion of employees who purchase the supplemental policy Let X and Y have the joint density function f(xy) = 2(x + y) on the region where the density is positive Given that 10% of the employees buy the basic policy, calculate the probability that fewer than 5% buy the supplemental policy E 0.417 0.500 E 0.108 n0.010 0.013 An auto insurance policy will pay for damage to both the policyholder's car and the other driver's car in the event that the policyholder is responsible for an accident The size of the payment for damage to the policyholder's car, X, has a marginal density function of for < x < Given X = x, the size of the payment for damage to the other driver's car, Y, has conditional density of for x < y < x +1 Given that the policyholder is responsible for an accident, calculate the probability that the payment for damage to the other driver's car will be greater than 0.5 E] 15/16 3/8 7/8 E 1/2 03/4 An insurance company's annual profit is normally distributed with mean 100 and variance 400 Let Z be normally distributed with mean and variance and let F be the cumulative distribution function of Z Determine the probability that the company's profit in a year is at most 60, given that the profit in the year is positive ten ngttai de/MSCB: Nguy'n Van Thin H9 ten ngit6i duA't HQ Chit kSr• Chit' kSr: (De thi gem g trang) [Trang 2/g 0,0C K H 04 66 TRUONG DAI C HO KHOA HOC TV'NHIEN, DHQG-HCM MA LUU TRU 0 c HOCIII MINN Dk THI KkT THUC HQC PHAN Hoc 16T II — Nam hpc 2017-2018 (do phong KT-DBCL Ott) An insurance agent offers his clients auto insurance, homeowners insurance and renters insurance The purchase of homeowners insurance and the purchase of renters insurance are mutually exclusive The profile of the agent's clients is as follows: i) 17% of the clients have none of these three products ii) 64% of the clients have auto insurance iii) Twice as many of the clients have homeowners insurance as have renters insurance iv) 35% of the clients have two of these three products v) 11% of the clients have homeowners insurance, but not auto insurance Calculate the percentage of the agent's clients that have both auto and renters insurance 1=17% E 28% El 10% E] 16% 11 25% In a shipment of 20 packages, packages are damaged The packages are randomly inspected, one at a time, without replacement, until the fourth damaged package is discovered Calculate the probability that exactly 12 packages are inspected [1 0.237 11 0.119 El 0.079 11 0.358 00.243 An auto insurance company insures an automobile worth 15,000 for one year under a policy with a 1,000 deductible During the policy year there is a 0.04 chance of partial damage to the car and a 0.02 chance of a total loss of the car If there is partial damage to the car, the amount X of damage (in thousands) follows a distribution with density function 0.5003e-42 < x < 15 (x) = 0 otherwise Calculate the expected claim payment 380 1:11 540 328 11 352 I11320 G An investment account earns an annual interest rate R that follows a uniform distribution on the interval (0.04, 0.08) The value of a 10,000 initial investment in this account after one year is given by V = 10, 000eR Let F be the cumulative distribution function of V Determine F(v) for values of v that satisfy < F(v) < 10, 000ev/ m000 10,408 25 425 25ev/io,000 — 0.04 El 25 [1n( v ) 0.04] 10, 000' v— 10, 408 10,833 — 10,408 Let X and Y denote the values of two stocks at the end of a five-year period X is uniformly distributed on the interval (0, 12) Given X = x, Y is uniformly distributed on the interval (0, x) Calculate Cov(X, Y) according to this model 24 E Mi [16 E 12 De thi g6m trang) [Trang 2/8] Oc K", 00 etocmtuititt DHQG-HCM MA Ulu TRe TRUON G DAI HOC KHOA HOC T V (do phOng KT-DBCL ghi) DE THI KkT TH-OC HQC PHAN Hoc kST II - Nam hoc 2017-2018 An insurance company categorizes its policyholders into three mutually exclusive groups: highrisk, medium-risk, and low-risk An internal study of the company showed that 45% of the policyholders are low-risk and 35% are medium-risk The probability of death over the next year, given that a policyholder is high-risk is two times the probability of death of a mediumrisk policyholder The probability of death over the next year, given that a policyholder is medium-risk is three times the probability of death of a low-risk policyholder The probability of death of a randomly selected policyholder, over the next year, is 0.009 Calculate the probability of death of a policyholder over the next year, given that the policyholder is high-risk E] 0.0025 El 0.3750 11] 0.0200 J0.1215 L10.2000 Each week, a subcommittee of four individuals is formed from among the members of a committee comprising seven individuals Two subcommittee members are then assigned to lead the subcommittee, one as chair and the other as secretary Calculate the maximum number of consecutive weeks that can elapse without having the subcommittee contain four individuals who have previously served together with the same subcommittee chair 1210 El 140 El 840 1J420 E170 10 Six claims are to be randomly selected from a group of thirteen different claims, which includes two workers compensation claims, four homeowners claims and seven auto claims Calculate the probability that the six claims selected will include one workers compensation claim, two homeowners claims and three auto claims Lj0.245 110.643 [1] 0.025 n 0.153 EI0.107 11 Ten cards from a deck ofplaying cards are in a box: two diamonds, three spades, and five hearts Two cards are randomly selected without replacement Calculate the variance of the number of diamonds selected, given that no spade is selected El 0.34 El 0.32 11 0.28 1110.24 rj 0.41 12 The number of tornadoes in a given year follows a Poisson distribution with mean Calculate the variance of the number of tornadoes in a year given that at least one tornado occurs 2.66 El 3.00 Oil 1.73 [1] 3.16 111 1.63 13 A delivery service owns two cars that consume 15 and 30 miles per gallon Fuel costs per gallon On any given business day, each car travels a number of miles that is independent of the other and is normally distributed with mean 25 miles and standard deviation miles Calculate the probability that on any given business day, the total fuel cost to the delivery service will be less than E 0.23 El 0.13 • El 0.47 El 0.38 EJ 0.29 14 The joint probability density for X and Y is f (x, I 20e-(x+2), x > 0, y > otherwise Calculate the variance of Y given that X > and Y > El 0.50 El 1.00 n 3.50 El 0.25 11] 3.25 De thi gem trang) [Trang 3/8] „„oc Kt10, 6, TRUONG DAI HOC KHOA HOC TV' NHIEN, DHQG-HCM MA LU'U TRU TP.HOCHI MINH DE THI KkT THI:JC FIQC PHAN Hoc kST II — Nam hoc 2017-2018 (do phOng KT-DBal, gla.) 15 A policyholder has probability 0.7 of having no claims, 0.2 of having exactly one claim, and 0.1 of having exactly two claims Claim amounts are uniformly distributed on the interval [0, 60] and are independent The insurer covers 100% of each claim Calculate the probability that the total benefit paid to the policyholder is 48 or less El 0.400 E 0.892 ri 0.320 11] 0.924 [1] 0.800 16 Automobile policies are separated into two groups: low-risk and high-risk Actuary Rahul examines low-risk policies, continuing until a policy with a claim is found and then stopping Actuary Toby follows the same procedure with high-risk policies Each low-risk policy has a 10% probability of having a claim Each high-risk policy has a 20% probability of having a claim The claim statuses of polices are mutually independent Calculate the probability that Actuary Rahul examines fewer policies than Actuary Toby n 0.2857 0.3571 11 0.3333 1:1 0.4000 [I] 0.3214 17 A company offers a basic life insurance policy to its employees, as well as a supplemental life insurance policy To purchase the supplemental policy, an employee must first purchase the basic policy Let X denote the proportion of employees who purchase the basic policy, and Y the proportion of employees who purchase the supplemental policy Let X and Y have the joint density function (xy) = 2(x + y) on the region where the density is positive Given that 10% of the employees buy the basic policy, calculate the probability that fewer than 5% buy the supplemental policy 0.010 El 0.013 1110.500 El 0.108 ri 0.417 18 An auto insurance policy will pay for damage to both the policyholder's car and the other driver's car in the event that the policyholder is responsible for an accident The size of the payment for damage to the policyholder's car, X, has a marginal density function of for < x < Given X = x, the size of the payment for damage to the other driver's car, Y, has conditional density of for x < y < x + Given that the policyholder is responsible for an accident, calculate the probability that the payment for damage to the other driver's car will be greater than 0.5 11 15/16 M 3/4 CI 1/2 E 7/8 E 3/8 19 An insurance company's annual profit is normally distributed with mean 100 and variance 400 Let Z be normally distributed with mean and variance and let F be the cumulative distribution function of Z Determine the probability that the company's profit in a year is at most 60, given that the profit in the year is positive F(2)/F(5) 11] [F(5) — F(2)1/F(5) E [1 — F(2)]/F(5) 11] — F(2) [F(0.25) — F(0.1)1/F(0.25) 20 A car is new at the beginning of a calendar year The time, in years, before the car experiences its first failure is exponentially distributed with mean Calculate the probability that the car experiences its first failure in the last quarter of some calendar year 111 0.102 11 0.205 EI 0.088 El 0.081 rm 0.250 (D8 thi dim trang) Prang 4/8] TRVONG DAI HOC KHOA HOC TV NHIEN, DHQG-HCM MA LUU TRU 0,pc KHQ, 5-, THI KkT THUG HQC PHAN H9c kr II - Nam hoc 2017-2018 (do ;doing KT-DBCI ghi) 21 The working lifetime, in years, of a particular model of bread maker is normally distributed with mean 10 and variance Calculate the 12th percentile of the working lifetime, in years 8.41 E 12.35 Ei 5.30 E 7.65 14.70 22 Individuals purchase both collision and liability insurance on their automobiles The value of the insured's automobile is V Assume the loss L on an automobile claim is a random variable with cumulative distribution function F(1) = (,1 )3-(1 - V)