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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)”
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: 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 Fdistribution 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 changeofvariable 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.
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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.
 Spring '08
 AlexeiStepanov
 Statistics, Probability

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