Question

Let X1, X2, ..., Xn be a random sample of size n from the distribution with probability density function

Inr 7- 1,0> 1 fx(x)fx(r; 0) (0-1)2 *

To answer this question, enter you answer as a formula. In addition to the usual guidelines, two more instructions for this problem only : write  $\prod_{i=1}^{n}(x_{i})$ as single variable p and $\bar{x}$ as m. and these can be used as inputs of functions as usual variables e.g log(p), m^2, exp(m) etc. Remember p represents the product of $x_{i}$ s only, but will not work for the product of any function of $x_{i}$ .

1. Find the maximum likelihood estimator of $\theta$

2. Suppose $\theta > 2$ . Find the method of moments estimator of $\theta$ . Use the sqrt(x) formula for square root.

Answer 1

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