Calculate the MLE of $1/\lambda$ for exponential distribution

Question

I have a sample of $n > 2$ independent and identically distributed random variables $Y_1, \ldots, Y_n$ from an $\exp(\lambda)$ distribution.

I know that the MLE of $\lambda$ is

$$\lambda = \frac{n}{\sum\limits_{i=1}^n y_i}$$

I want to calculate the MLE of $1/\lambda$. Any hints where to start? Can I use the likelihood function?

Answer 1

A useful fact about MLEs you can prove with the chain rule is that $\widehat{f(\lambda)}=f(\widehat{\lambda})$. Therefore, $\widehat{\frac{1}{\lambda}}=\frac{1}{n}\sum_{i=1}^ny_i$.