Suppose you've a coin that is not a fair coin, and that it is known that the probability p of seeing heads in one coin toss is either 1/4 or 3/4. Let Y be the number of heads observed in two coin tosses. For each possible value of Y, which value of p (of the two possible choices, p=1/4 or p=3/4) maximizes the probability that Y=y?
Depending on the value of y actually observed, what is the MLE of p?