3: MLE and MAP estimates (SEng 474: 10 points; CSc 578D: 15 points) a) Let = P(X=T). Calculate the MLE for for the following dataset by finding the maximum of PDI ). Show your work. [4 marks] D-{T, T,T,T, T, T, T, F,F, Fy b) Recall the PDF for a Beta random variable is proportional to Q3l-) *(1- 0)(821) (2-1) with parameters 1 and 2. Let's say you have evidence from previous studies that P(X=T) = . Let 1 4. Find 2 and then calculate the MAP estimate P(J 1 D) for with a Beta(1 , 2) prior and the dataset above. Show your work. [6 marks]