Let X1, X2, ... , Xn be a random sample from a distribution with pdf f(x; ) = x1, 0 < x

Chapter 6, Problem 6.7-4

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QUESTION:

Let X1, X2, ... , Xn be a random sample from a distribution with pdf f(x; ) = x1, 0 < x < 1, where 0 < . (a) Find a sufficient statistic Y for . (b) Show that the maximum likelihood estimator 6 is a function of Y. (c) Argue that 6 is also sufficient for .

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QUESTION:

Let X1, X2, ... , Xn be a random sample from a distribution with pdf f(x; ) = x1, 0 < x < 1, where 0 < . (a) Find a sufficient statistic Y for . (b) Show that the maximum likelihood estimator 6 is a function of Y. (c) Argue that 6 is also sufficient for .

ANSWER:

Step 1 of 4

Given:

An i.i.d. sample of random variables   have the following density function:

                                               

 

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