Let $Y_1,\ldots,Y_n$ denote a random sample of size $n\ge4$ from Bernoulli ($\theta$) distribution where $$0 < \theta < 1$$ is the success probability.
How would I derive the maximum likelihood estimator (MLE) of $\theta^2?$
Also, with $\hat{\theta}=Y_1Y_2$ being unbiased for $\theta^2$, and $U=\sum(Y_i)$ is a minimal sufficient statistic for $\theta$, how would I "Rao-Blackwellize" $\hat{\theta}$ and explicitly derive the conditional expectation, $E[\hat{\theta}|U]$, to come up with the minimum variance unbiased estimator (MVUE) for $\theta^2?$
These questions are confusing me because it is asking for $\theta^2$ instead of just $\theta$. If someone could please show/tell me what to do/steps to figuring this out that would be amazing!