Dr. Hackney STA Solutions pg 39

# Dr. Hackney STA Solutions pg 39 - 3-12 Solutions Manual for...

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Unformatted text preview: 3-12 Solutions Manual for Statistical Inference b. 0 = 2 2 k h(x)c() exp i=1 k wi ()ti (x) dx = h(x)c () exp i=1 wi ()ti (x) dx k k + h(x)c () exp i=1 k wi ()ti (x) i=1 k wi () ti (x) dx j wi () ti (x) dx j 2 + h(x)c () exp i=1 k wi ()ti (x) i=1 k + h(x)c() exp i=1 k wi ()ti (x) i=1 k wi () ti (x) j dx + h(x)c() exp i=1 2 wi ()ti (x) i=1 k 2 wi () ti (x) dx 2 j = h(x) 2 logc() c() exp j 2 k wi ()ti (x) dx i=1 + c () h(x) c() c() exp i=1 k wi ()ti (x) dx +2 logc() E j k i=1 wi () ti (x) j k +E ( i=1 2 wi () ti (x))2 + E j 2 i=1 2 wi () ti (x) 2 j = 2 logc() + logc() j j k -2E i=1 k wi () ti (x) E j k i=1 wi () ti (x) j k +E ( i=1 wi () ti (x))2 + E j k i=1 2 wi () ti (x) 2 j k = 2 2 logc() + Var j k wi () i=1 j ti (x) i=1 2 wi () ti (x) j +E i=1 2 wi () ti (x) . 2 j . Therefore Var = - 2 logc() - E j k 2 wi () ti (x) 2 i=1 j 1 2 , 3.33 a. (i) h(x) = ex I{-<x<} (x), c() = (ii) The nonnegative real line. 1 2 exp( - ) > 0, w1 () = 2 t1 (x) = -x2 . 1 b. (i) h(x) = I{-<x<} (x), c() = 2a2 exp( -1 ) - < < , a > 0, 2a 1 1 w1 () = 2a2 , w2 () = a , t1 (x) = -x2 , t2 (x) = x. (ii) A parabola. ...
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## This note was uploaded on 02/03/2012 for the course STA 1014 taught by Professor Dr.hackney during the Spring '12 term at UNF.

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