1- Assume we have two random variables X and Y. They have no conditional or unconditional dependencies. What is the numerical value of the following sentence? Justify your answer. [10 points] i P (X=i | Y=y)

2- Assume M is an event which has a 50% chance (equivalent to 1/2) to happen. N is another event which may happen 33.33 % (equivalent to 1/3) of the times. We also know that the chance of M happening given that N does not happen is 25% (equivalent to 1/4). What is the chance of M happening given that N happens? Show your work. [20 points]

3- Draw the resulting Bayesian network from the following sentence. [15 points]

P(Q) P(X | Q) P(Y) P(W | Q,X,Y) P(Z | X,W) P(G | Y,W,Z) P(M | W)