# Maximum Likelihood Estimator

1. Nov 25, 2009

### cse63146

1. The problem statement, all variables and given/known data

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).
2. Relevant equations

3. The attempt at a solution

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

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

2. Nov 25, 2009

### Temporaneo

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

3. Nov 25, 2009

### cse63146

you mean:

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

4. Nov 26, 2009

### Temporaneo

correct, i think

5. Nov 26, 2009

Thanks.