A 2 [13 marks] (a) Let X have pdf fx(x) = xye- for x > 0...

 

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A 2 [13 marks] (a) Let X have pdf fx(x) = x²y³e- for x > 0 where y € (0, ∞) is an unknown parameter. Compute the maximum likelihood estimator based on a random sample ₁,...,n of size ne N. You should carefully verify that your truly maximizes the likelihood (or log likelihood). [7] (b) [Type] Describe the three main favourable asymptotic properties of MLEs discussed in the course. For each of these properties, decide whether they are relevant in the example treated above and describe what they imply in this particular example. [6] A 2 [13 marks] (a) Let X have pdf fx(x) = x²y³e- for x > 0 where y € (0, ∞) is an unknown parameter. Compute the maximum likelihood estimator based on a random sample ₁,...,n of size ne N. You should carefully verify that your truly maximizes the likelihood (or log likelihood). [7] (b) [Type] Describe the three main favourable asymptotic properties of MLEs discussed in the course. For each of these properties, decide whether they are relevant in the example treated above and describe what they imply in this particular example. [6]

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a M LE 0 arg max log 2 ry e arg max r yl og 2 y log e arg max r yl og 2 y log e arg max y r log 2 lo... View the full answer