Dr. Hackney STA Solutions pg 99

Dr. Hackney STA Solutions pg 99 - 7-2Solutions Manual for...

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Unformatted text preview: 7-2Solutions Manual for Statistical InferenceFor the given data,n= 14 andixi= 323.6. Many computer programs can be usedto maximize this function. From PROC NLIN in SAS we obtain = 514.219 and, hence,=323.614(514.219)=.0450.7.3 The log function is a strictly monotone increasing function. Therefore,L(|x)> L(|x) if andonly if logL(|x)>logL(|x). So the valuethat maximizes logL(|x) is the same as thevalue that maximizesL(|x).7.5 a. The value zsolves the equation(1-p)n=Yi(1-xiz),where 0z(maxixi)-1. Letk= greatest integer less than or equal to 1/z. Then fromExample 7.2.9,kmust satisfy[k(1-p)]nYi(k-xi)and[(k+ 1)(1-p)]n<Yi(k+ 1-xi).Because the right-hand side of the first equation is decreasing in z, and becausek1/z(soz1/k) andk+ 1>1/z,kmust satisfy the two inequalities. Thuskis the MLE.b. Forp= 1/2, we must solve(12)4= (1-20z)(1-z)(1-19z), which can be reduced to thecubic equation-380z3+ 419z2-40z+ 15/16 = 0. The roots are .9998, .0646, and .0381,16 = 0....
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