Consider the following probability density function for the, Microeconomics

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Consider the following probability density function for the

Question: Consider the following probability density function for the random variable x:

a. Suppose a random sample of 5 observations on x yields data 1, .8, 1.3, 1.6, 2. What is the maximum likelihood estimate for θ?

b. Find the maximum likelihood estimator (MLE) for θ.

c. Is the MLE always the best choice for an estimator?

d. Outline how you would find a method of moments (MOM) estimator.

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