X X2 X- XA X X6 X7 Xg X9 X10 x: [1] 1 1 1 1 0 0 0 0 0 1 x, [2] 1.0 2.0 2.5 3.5 4.0 5.0 0.5 1.0 2.0 2.5 y1 V2 V4 V6 V7 y8 V9 y10 0 0 0 0 0 0 1 1 1 1 Figure 1: A two-dimensional labeled dataset with 10 data instances. instance X = x y = arg max p(Y = c(X = x) CE{0,1} = arg max p(Y = c) x p(X[d] = x[d]ly = c). CE {0,1} d=1 You will begin by estimating the parameters of . P(Y) . p(X[d]|Y = c) Vce {0, 1}, de {1, 2 } from the labeled dataset, using Maximum Likelihood Estimation (MLE). Note that, p(Y) is a Bernoulli distribution; p(X[1][Y = c) is a Bernoulli distribution of X[1]; p(X[2]|Y = c) is a Gaussian distribution of X [2]. (a) Prior distributions [2 points] What is p(Y = 1)? The answer is a real number. (b) Conditional distributions [5 points] What is p(X[1] = 1/Y = 0)? What is p(X [1] = 1/Y = 1)