The density function is given as:
$$
f(x|\theta) = \begin{cases}
\theta e^{-\theta x} & \text{if } 0 < x < \infty \\
0 & \text{otherwise}
\end{cases}
$$
Now, we need to find the joint density function of the random variables $X_1, X_2, \dots, X_n$. Since they
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