STAT 4201 Final: STAT 421 OSU Practice Final Exam-II
31 Jan 2019
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Recitation instructor (circle yours):lira pi/ siyoen kil/ rui wang. Show all of your work for partial credit. This is a closed book, closed notes, closed neighbor exam. You may use a calculator and 3 pages of notes. Suppose the variances are known and the common mean is unknown: and x2 be the sample, population. Assume the two random sample (a) (5 pts. ) Show that t1 = c x1 + (1 c) x2 where 0 c 1 is an unbiased estimator of . (b) (10 pts. ) Determine c such that var(t1) is the smallest. (c) (15 pts. ) Find a su cient statistic for . (b) (10 pts. ) Find the maximum likelihood estimator of : let x be a single observation from a population with pdf f (x; ) = ( e x, x > 0; > 0 otherwise. Consider testing the hypothesis h0 : = 2 against the alternative h1 : < 2.
