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sampexam1soln

# sampexam1soln - STAT 8260 Exam 1 — Thursday February 27...

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Unformatted text preview: STAT 8260 Exam 1 — Thursday, February 27 SHOW ALL WORK AASwer k N ammﬂgx 1. Let 3 0 6 A: 0 2 2 =(a1,a2,a3) 4 0 8 where a1,a2,a3 are the columns of A. Let V : £(a2,a3) and suppose y N N3(M,0‘213). a. (9 points) Find PV and Pam). V=Zf€~u6>5= Z (Queﬁ 5”“ a, c ’ COD .1. \$3,): 0 I 77 74/0: QQ’F‘ wkuz 9‘ {Hana ‘NI ”9:” AV, 0 _‘ 3/; o 3/5 O 7/5’ 7/23” o ”72\$" -— /}2‘ i > (9 l O .6 (9 l o O b. (7 points) Find the eigenvalues (and their multiplicities) of PV. ﬂ” QIJMValu/CS‘ “ff; .(9 C: an“ “5 0'0 m3 ﬂayed/9,. Ma 272 («l/ AMI/{Maul 0/ / efw/ 74> can (V) SO % WJMVa/Ugj We / ) W/W/%/Aa§ elm/v): “J (9/ w/ Mu/éluﬁ / c. (7 points) Are yTPVy and y — A(ATA)"ATy independent? Why or w new; = (1: ~ afé‘m‘é‘w V‘W Sm“. \$1.3, 2Q ) >gj aremoé/eao/M/t d. (7 points) What is the distribution of Flglly —— CH2, where c is a 3 X 1 vector of constants? 55 //g ‘— g// 1 : ﬂaw Wag/«g , #52 . W ”ltw’é)??? . 5/466 I) 7% M747}? //\ % 7%Jfk7gc Aim (:2 I3 M/évyewévv/ w/ ”WA 3 :5 Eager~>C’(3,9:i?~lxé>%é\> , 9273);}.ﬂ/wé/W e. (7 points) Now suppose p, = (1/3, 0, —1/4)T and ﬁnd E(yTPVy). 5/1“? 3% i? (R 03f) + Avg/9. ‘L L' :az7lv/R>+//E,/g//z prﬂVC/‘V’ 11\$ mv [171/5 WI oc/ﬂsaona/ 7Z2? 50% .4. 1""sz :zcl‘M(V):2 whim a 5 L wt 5‘ gas” gr V) «)1 :25 - i 73 {(37%sz “PM“ 9 a. (6 points) Which pairs of variables in y are independent? ‘4‘ 3?” are MJﬁN/VJWJ/ I b. (Jr; points) Find the distribution of ( Z2) . , 3 ' W911): €/§:)+ W: C. Q8‘points) Find the par rtial corr leaiot on coe fﬁci ent p23“ (p2 2.3 1 in our book’ 3 notation). ,(00‘ (7117:” @7097/u] 'IQEM V“( (3:) V1 « \ __~ A a”) “3“ " W -.. ~— .; 1 ~15 ’\ S‘ J? 3. Let X1 ..... Xn and Y1, . . ..,Yn be_independent random} samples from N (111,02) and N(u2, 202), respectively. Let X = \$22; X,- and Y = \$22; 12.. a. (8 points) Find the distribution of 2:?=1(Xi — {2)2 221:1”; - W2 ' A 7’ 2 w- 1 f 3’; £06133”?! #2)). \$2M”) ”7L A D F \ male/AwQM/fl'b b. (8 points) Find the mean and variance of 31-2- 2% - XV + 5%,; Zn:- — W. i=1 i=1 ABA ’- ./ a. (8 points) Show that B is a generalized inverse of A. , o .. 7 O J «2i?! 1 ) I -1 :i,‘ 1 K \J 7, ,. 3/ o 3 3 I) 3 I 0 313> {1’3 . ‘ i \ {/3 r ’5»; points) Show that Ax = c is not a consistent system of equations. Cons'sz'nﬂl I‘fp A/rcac. I47” “3 W‘i/Iw. Int/UM #— of ,4. 50 cl‘ué 7/ 43¢ C 47576: H :} 7 mw IS. 40/ was/:45/ c. (6 points) Change c so that the system Ax = c is consistent. A’ til/13"?) ; (a): lbw“ 7679/ 4 5"‘3 “Jr / N0743€ ’53) 3 1Q, +g7, 31714; Ad: :9 710 A? wasvawﬂﬁzeysz >562, SW Fe/cu749454p m Aﬁgs [/1 3.4 WS/ Zn/O/“A E £71 n) mar/Z {ave C = 1C,+C2 3 50 g 2 I) (ANN mp4 3 _____l_____________mm_.~7_w_,m ...
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sampexam1soln - STAT 8260 Exam 1 — Thursday February 27...

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