AMU 2025 — Mathematics PYQ

Let $X_1,X_2,\dots ,X_n$ be i.i.d. random variables having pdf f(x) = \frac{1}{\theta} e^{-x/\theta}, \quad 0 < x < \infty,\; \theta > 0 The cdf of the largest order statistic  
$X_{(n)}=\max (X_1,X_2,\dots ,X_n)$ is: