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hw5 - 36-226 Summer 2010Homework 5Due July 141 LetX1,Xnbe...

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Unformatted text preview: 36-226 Summer 2010Homework 5Due July 141. LetX1,...,Xnbe independent butNOTidentically distributed. LetXi∼Normal(μi,1)(that is eachXihas a different meanμi).(a) Write down the likelihood and loglikelihood.(b) Find the MLE for the vectorμ= (μ1,μ2,...,μn).(c) Find the MSE for the MLE (this should be really easy).(d) Another estimator forμisbμSi=Xii∈Si6∈S,forSsome subset of the integers 1,...,n. For example,S={1,5,6,7,9}. Find theMSE for this estimator (the general one, notS={1,5,6,7,9}).Hint:Here it is easier to find the MSE directly rather than finding the bias and varianceseparately.Comment:This problem is not hard, it just requires thought about what you are tryingto find. Think about what the math means and use your understanding of the material toanswer the question rather than trying to blindly apply a solution algorithm.2. Small planes cannot fly well if the cargo (people and luggage) weighs too much. Supposethat an airline runs a commuter flight that holds 36 people. It is known from past experiencethat an airline runs a commuter flight that holds 36 people....
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