STAT 4201 Final: Statistics 421 Practice_Final_Exam-I
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. Max time: 108 minutes; max points: 150: let x1, . , xn be a random sample from a population with pdf f (x; ) = ( x 1 0 < x < 1; > 0 otherwise. Find a su cient statistic for . (b) (10 pts. ) 1: let x1 and x2 be the means of independent random samples of size n and 2n from a n ( , 2) population. (a) (5 pts. ) Show that t1 = c x1 + (1 c) x2 is an unbiased estimator of for any real c. (b) (12 pts. ) Determine c such that var(t1) is the smallest and give an explicit expression for the estimator t . 1 that corresponds to the minimum variance. (c) (13 pts. )
