Maximum Likelihood estimate of $\theta = p^2$ for Bernoulli distribution

Question

Question:

For a Bernoulli population, show that the maximum likelihood estimate of $\theta =p^2$ is $\bar{x}^2$.

I'm just looking for a hint to get started.

Obviously, I can find the MLE of a Bernoulli by maximizing the likelihood function. How can I maximize $\theta = p^2 $ if $p^2$ is not in the original distribution

Answer 1

Note that if $\alpha$ is the MLE of $\beta$ , for any function $f(\alpha)$ is MLE of $f(\beta)$. Just consider $f(x)=x^2$.