a) Let 0 = P(X=T). Calculate the MLE for 0 for the following dataset by finding the maximum of P(DI 0). Show your work. [4 marks] D={T, T, T, T, T, T, T, F, F, F} b) Recall the PDF for a Beta random variable is proportional to (1-1) * (1-0)(2-1) with parameters 1 and 2. Let's say you have evidence from previous studies that P(X=T) = 12. Let 1 = 4. Find 2 and then calculate the MAP estimate P(0 | D) for 0 with a Beta(B1, B2) prior and the dataset above. Show your work. [6 marks]