312-midterm2sol - Stat312 Midterm I Solution Moo K Chung Yulin Zhang [email protected] [email protected] March 5 2003 1 Let X1 Xn be a random

312-midterm2sol - Stat312 Midterm I Solution Moo K Chung...

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Stat312: Midterm I Solution Moo K. Chung, Yulin Zhang [email protected], [email protected] March 5, 2003 1. LetX1,· · ·, Xnbe a random sample from Bernoullidistribution with parameterp.(a) What is(S2/p2)?S2is the sample variance. Ex-plain your results (10 points).(b) Find an unbiased estimator ofp2.Explain yourresults (5 points). 2. LetX1, X2be a random sample fromN(0,1). Notethat the sample size is 2 and the density function forXiisf(xi) =θ2πexp(-θx2i/2).(a) Obtain an estimator ofθusing the method of mo-ments. Explain your results (5 points).(b) Find the likelihood function and use it to obtain the

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