# HW3 - HW#3 Due Friday October 14 by noon(slip under...

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1 HW #3 Due Friday, October 14, by noon (slip under instructor’s door, if not in office) Read the rest of Sections 6.2 and 6.4 (for asymptotic distribution of MLEs) and the class notes Notes_3 up to the section titled "Critical Regions from Asymptotic Dist. of LRs" (for asymptotic distributions and inverting hypotheses tests). Problems 1—3 are due on the due date. Problems 4—5 are practice problems that you do NOT have to turn in (but you should do them in preparation for the midterm). 1) For { X i : i = 1, 2, . . ., n } a random sample from an N ( µ , σ 2 ) population, invert an appropriate LRT to give a one-side upper CI on with unknown for some specified confidence level α . Show every step of the process (i.e., do not just state the final form of the CI). 2) Let { X i : i = 1, 2, . . ., n } be a random sample from a Bernoulli population with probability of success p (= Pr { X i = 1} ). Invert an appropriate LRT to give a one-side lower CI on p for some specified confidence level . Show every step of the process (i.e., do not just state the final form of the CI). 3) Let { X i : i = 1, 2, . . ., n } be a random sample from an N ( , 2 ) population. Sometimes one is interested in the ratio / , which is called the coefficient of variation . The coefficient of variation can be viewed as a normalized (by the mean), dimensionless version of the standard variation. One usually calculates the coefficient of variation only for nonnegative data.

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