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Question 5 (20 points) a) Given the following Bayes Net and CPTS (conditional probability tables), calculate the following quantities (6 points): (i) P(+b|+a)= (ii) P(+a,+b)= (iii) P(+a+b)= PLAY + 0.25 PEBAY +6 PICJA) + +e 05 0.5 + 075 -0 0.25 0.75 1 02 08 06 04 PDM) + KEB - +6 06 04 -b 08 0.2 +5 → 0.25 075 01 0.9 Consider the following Bayes Net b) Express the joint probability distribution as a product of terms representing individual conditional probabilities. (4 points) c) You are building advanced safety features for cars that can warn a driver if they are falling asleep (A) and also calculate the probability of a crash (C) in real time. You have at your disposal 6 sensors (random variables): ⚫ E: whether the driver's eyes are open or closed • W: whether the steering wheel is being touched or not • L: whether the car is in the lane or not ⚫ S: whether the car is speeding or not • H: whether the driver's heart rate is somewhat elevated or resting • R: whether the car radar detects a close object or not A influences (E,W,H, L,C). C is influenced by (A, S, L., R). Draw the Bayes Net associated with the description above by adding edges between the provided nodes where appropriate. (10 points)

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