# Monrad.410.16 - STAT W0 / MATH L{é‘{ . I? X1 cg, “1M W...

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Unformatted text preview: STAT W0 / MATH L{é‘{ . I? X1 cg, “1M W MWLL ~. fth/Avq’t (21 WW = E(e"‘x‘+£2X2) = <l>1e*‘+ plain p3)” (su Mg 139.) 1+ (WM WM (501 ML 106.) €093 = ﬁﬂﬁuﬂlmﬂ = “P, E09 = EEWwEUJcJItFW = mp; EOQXD = ﬁméiﬁ) {124:0 ‘1 “(n'DRPz CNOQQQ = 13099) 'E(X15E(Xz) = “(n-0W - “\$192 = ma- :E (MC/£56: 5.1L; V ‘ Each. ﬁle 30H¢Lﬂa¢ Caz/3f W W J km “W W417) , ﬁat/m?) ham m (ARA. 5% a .138 439.“. ' with Hagan?) I P1. é§,) 316:.5,/é.3)) .. STAT Lilo / MATH 444 EXQQKQ ;§.3¢ZS 2M W ‘m {If ELSA/V1 "We, WWW « m in a W3 1! . m4 may , mﬁﬁfﬁwg? W Ywé w; W2 Wé’mm LL «W4 a name/5m {VA/(75> " " .. 11”“ X1 is 115201) Md Y/ Es Xzﬂ’) I m (7% r, <1 r J M M #8 -= Myaﬁ / W [19) =2 («M/2- / mam/z (7»zt>"["“‘>/2— , gr Ma, This Sada/3 W is XZKF'ﬂ>. : ioiifocxpﬂ- (1x4— 5.3/2)Z - 217de 4 ~Zz/H/ w , ' z : ﬁe eSUP[-(?<~Z/Z) de Er 0mg) Mica 0? W1 Cms‘wqh d>O and ﬂ) ?5%‘WP[‘(X‘ﬂ>Z/<Zdl)]ob< = 1, ~00 00 50 S wL—‘(Xv—k/ABZ/(zdzﬂa‘x <5 27*“ an n ,S i l€m€v€ #:2/1 W dz M w SUP["(W~Z/z)2]g(x g ~CO So ~oo<2z<oo) _ 2/LI 00 ' 2 gm 2 ﬁe? .Swp[-—(?<~z/Z‘) M : W.€'ZZ/L‘ z 1 ,e'ZZ/(z‘m‘ 2’“— Viv—275‘ TMS is PM ma Hm N.<O,Z>0€is‘“riba}§0m 3.6.8 Since F = 57/}; then 21,: 2: g :3, which has an F-distribution with r2 and r1 degrees of freedom. 3.6.10 Note T2 = Wz/(V/V‘) = (W2/1)/(V/T). Since W is N(O, 1), then W2 is X2(1), Thus T2 is F With one and 7‘ degrees of freedom. 3.6.12 The change-of-variable technique can be used. An alternative method is to observe that Where V and U are independent gamma variables with respective parameters (73/2, 2) and (73/2, 2). Hence, Y is beta with a = r2/2 and ﬂ = r1/2. 3.6.14 For Part (a), the inverse transformation is 11:1 = (y1y2)/ (1 + yl) and x2 = y2/(1+ yl). The space is y,- > O, i = 1,2. The Jacobian is J = 312/“ + .7102. It is easy to show that the joint density factors into two positive functions, one of which is a function of y1 alone while the other is a function yg alone. Hence, Y1 and Y2 are independent. (la) Tim hwsf-ormcthn tar—«mag in Sacha/u 2,7 Cam he (meal in Shm Y4} Y2) and X5 M mix/mils [hwy/4.40mi (U§ gﬁflﬁf SW Jacoéiah M in Paul” 4 gta » an >25 = Walgzﬁzl 'jg/Xg) “at Mr ai of“ Y: l/Z daiX NMO wusiolmd’oih F ii " J h ‘3 Na 354/03 SW «Lam/4 since Y Y W X ara Z whaﬂa (Makjbwdemﬂ’ z‘xt WM) W3 . T1 = MYA and T2 = ﬁgs/2%; 'mdxpwdmt Ma mi 3% W PM: 5 m J 7; a 9%, = My x4)P(—géxaj Er m3 chow. o€ Ag W X2. [Sea 7km 25.2) m )2 e m = sks<ggahgﬂmdg¢>gwg = 311% § 31333.;(32) 33(315 pg“) @631 aaé ._._. ﬁg ( \$1 3,1343%)3.43.1333“; Amﬁ = (s; w; ow mm ...
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## This note was uploaded on 06/11/2010 for the course STAT 410 taught by Professor Alexeistepanov during the Spring '08 term at University of Illinois at Urbana–Champaign.

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Monrad.410.16 - STAT W0 / MATH L{é‘{ . I? X1 cg, “1M W...

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