## Maximum likelihood, moments, and the mean of a Poisson

If we observe data coming from a distribution with known form but unknown parameters, estimating those parameters is our primary aim. If the distribution is uniform on $[0,\theta]$ with $\theta$ unknown, we already looked at two methods to estimate $\theta$ given $n$ i.i.d. observations $x_1,\dots,x_n$: Maximum likelihood, which maximizes the likelihood function and gives $\max\{ […]