Question: 6.2.7 If (x1, .. ., xn) is a sample from a Beta(a, 1) distribution where a > 0 is unknown, then determine the MLE of

6.2.7 If (x1, .. ., xn) is a sample from a

6.2.7 If (x1, .. ., xn) is a sample from a Beta(a, 1) distribution where a > 0 is unknown, then determine the MLE of a. you can express the pdf in a form that does not have gamma functions. (What is the right constant so it integrates to 1?) . It may help to identify the distribution of Yi = -log(Xi) (and hence its mean and variance). (a) Show that the MLE for a is consistent. (b) Also, find the Fisher information and determine the asymptotical normal distribution for the MLE of a

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