One observation is taken from a discrete distribution with a parameter $\theta$. There are 3 possible values of $\theta$: 1, 2, and 3. The PMF is given below.
What is the MLE of $\theta$?
I suspect that $X = 3$ has something to do with the answer, because it has non-zero probabilities for all 3 values of $\theta$.
I also know that the MLE cannot be terribly complicated, because there is only one observation to work with.