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### Finding the Maximum Likelihood Estimator (MLE)
Consider a random sample \(x_1, x_2, ..., x_n\) from the following probability density function (pdf):
\[
f(x) =
\begin{cases}
\theta x^{\theta - 1} & \text{if } 0 \leq x \leq 1 \\
0 & \text{otherwise}
\end{cases}
\]
where \(\theta > 0\).
Find the maximum likelihood estimator for \(\theta\).
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