Question

The random variable X has probability density function
fX(x) = (theta)x^((theta)-1); 0 <=x<= 1;
with parameter  (theta)> 0. A random sample of n observations, X1; X2; : : : ; Xn, is selected from
this distribution.
(i) Write down the likelihood function and use it to find the maximum likelihood estimator for (theta). Check that the likelihood is maximised at this point.
(ii) A random sample of size 4 yields product(i=1 to 4)xi of 0.6. Estimate (theta).