Mathematics, 13.05.2020 01:57 Amholloway13
[This problem is about (1) UMP hypothesis tests and (2) confidence intervals obtained by inversion. And a Bayes credible interval (set).] Let X1,...,Xn be a random sample from the density f(x|ā) = ā2 xeāxI(0,1)(x), where ā¦ = {ā : ā > 0} is the parameter space. a) Consider the problem of testing H0 : ā = ā0 versus H1 : ā 6= ā0. Derive the size āµ likelihood ratio test of these hypotheses. Show that the rejection region can be written in terms of the statistic Pn i=1 Xi. Give an explicit form for the rejection region in terms of percentiles of a 2 distribution. Hint: The random variable 2ā Pn i=1 Xi has a chi-square distribution with 4n degrees of freedom. b) Now consider testing H0 : ā ļ£æ ā0 versus H1 : ā > ā0. Doe
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Mathematics, 21.06.2019 20:40
If the endpoints of the diameter of a circle are (8, 6) and (2,0), what is the standard form equation of the circle? a) (x + 5)2 + (y + 3)2 = 18 (x + 5)2 + (y + 3)2 = 3.72 (x - 5)2 + (y - 3)2 = 18 d) (x - 5)2 + (y - 3)2 = 32
Answers: 1
[This problem is about (1) UMP hypothesis tests and (2) confidence intervals obtained by inversion....
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