## Maximum Likelihood Estimator

Suppose X1...Xn are iid and have PDF $\displaystyle f(x; \theta) = \frac{1}{\theta} e^{\frac{-x}{\theta}} \ \ \ 0<x<\infty$

Find the MLE of P(X<2).

I know the MLE of theta is $\displaystyle \overline{X}$

so would $\displaystyle P(X<2) = 1 - \frac{1}{\overline{X}} e^{\frac{-2}{\overline{X}}}$?