312-midterm2 - Stat312 Sample Midterm II Moo K Chung 1 Let X1 Xn be a random sample from Bernoulli distribution with parameter p(a Compute a 95 condence

312-midterm2 - Stat312 Sample Midterm II Moo K Chung 1 Let...

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Stat312: Sample Midterm II Moo K. Chung September 30, 2004 1. LetX1,· · ·, Xnbe a random sample from Bernoullidistribution with parameterp.(a) What isE(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 themaximum likelihood estimator ofθ. (5 points foreach question).

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