Finding the MLE for a Given Probability Using iid PDF

[cse63146]

Homework Statement

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

Find the MLE of P(X<2).

Homework Equations

The Attempt at a Solution

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

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

Thank you in advance.

 

[Temporaneo]

nope, i think you should use the integral of pdf. the pdf is like the puntual probability of value x.

 

[cse63146]

you mean:

$$1 - e^{\frac{-2}{\overline{X}}}$$

 

[Temporaneo]

correct, i think

 

[cse63146]

Thanks.