Problem 3 [10 points] Bayesian Network. Suppose that most morning you set your alarm for 8am...

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Problem 3 [10 points] Bayesian Network. Suppose that most morning you set your alarm for 8am so that you can catch the 8:30am bus to school which usually arrives just in time for your class at 9am. Unfortunately, sometimes you forget to set your alarm which might make you miss your bus and this increases the probability that you are late for class. Even if you catch the 8:30am bus, there's a chance you'll be late for class. To help analyze the situation we introduce some random variables. Let A = 1 if you remember to set your alarm and A = 0 otherwise. Let B = 1 if you catch the 8:30am bus and B = 0 otherwise. Let L = 1 if you are late for class and L = 0 otherwise. Suppose that P(A = 1) = 3/4, P(B = 1|A = 1) = 4/5, P(B = 1|A = 0) = 2/5, P(L = 1|B = 1) = 1/4, and P(L = 1|B = 0) = 2/3. 1) What are the values of: P(A = 0), P(B = 0|A = 1), P(B = 0|A = 0), P(L=0|B = 1), and P(L=0|B = 0) ? 2) Draw the Bayesian network for the random variables A, B, and L. 3) What is the value of P(A = 1, B = 1, L = 0)? 4) What is the value of P(B = 1)? 5) What is the value of P(L = 0)? 6) What is the value of P(L = 1, A = 0)? 7) What's the value of P(L = 1|A = 0)? Problem 3 [10 points] Bayesian Network. Suppose that most morning you set your alarm for 8am so that you can catch the 8:30am bus to school which usually arrives just in time for your class at 9am. Unfortunately, sometimes you forget to set your alarm which might make you miss your bus and this increases the probability that you are late for class. Even if you catch the 8:30am bus, there's a chance you'll be late for class. To help analyze the situation we introduce some random variables. Let A = 1 if you remember to set your alarm and A = 0 otherwise. Let B = 1 if you catch the 8:30am bus and B = 0 otherwise. Let L = 1 if you are late for class and L = 0 otherwise. Suppose that P(A = 1) = 3/4, P(B = 1|A = 1) = 4/5, P(B = 1|A = 0) = 2/5, P(L = 1|B = 1) = 1/4, and P(L = 1|B = 0) = 2/3. 1) What are the values of: P(A = 0), P(B = 0|A = 1), P(B = 0|A = 0), P(L=0|B = 1), and P(L=0|B = 0) ? 2) Draw the Bayesian network for the random variables A, B, and L. 3) What is the value of P(A = 1, B = 1, L = 0)? 4) What is the value of P(B = 1)? 5) What is the value of P(L = 0)? 6) What is the value of P(L = 1, A = 0)? 7) What's the value of P(L = 1|A = 0)?

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1 The values of the probabilities are PA 0 1 PA 1 1 34 14 PB 0A 1 1 PB 1A 1 1 45 15 PB 0A ... View the full answer