A sample of 4 observations:
0.3, 0.6, 0.9, 0.5
is collected from a continuous distribution with density:
$$f(x) = \begin{cases} \theta x^{\theta - 1}, & \text{for } 0 < x < 1 \\ 0, & \text{otherwise} \end{cases}$$
(a) Estimate $\theta$ by the method of maximum likelihood. Round your answer to 3 decimal places.
(b) Recompute the estimator by using the method of moments. Round your answer to 3 decimal places.