Bayesian Probability and Independence in Engineering

Section A Consider the scenario where an engineering team is building a new product, a product manager designs the three components of the product, and 3 developers each implement one of the designs into a functionality, which combines into the product. Then the QA engineer examines the product for issues and a release of the product to customers occurs. The Pm, DV1, DV2, DV3, QAE nodes respectively denote the probability that those individuals are overworked. DS1, DS2, and DS3 marks whether each of the designs the product manager provided are correct. F1, F2, F3, denotes whether each of the three functionalities work correctly. P denotes whether the overall product functions correctly. QA denotes whether the Quality Assurance Engineer alerted there is an issue with the product. Lastly R denotes whether the product was released to customers. See the Bayes Net and the Probability Tables on the following pages. 6.A.1 Which of the following statements are true? Independence is represented as in the format in this example: A ? B | C means that A is independent of B given C. Mark all that apply. (2 points) ? F2 ? PM | DS2 ? F3 ? DS3 | PM ? P ? DV1 | F1, PM ? The intersection of the Markov blankets of F1 and F2 contain 3 nodes. ? P ? DV1, DV2, DV3 | F1, F2, DS3 ? PM is in the Markov blanket of F1 6.A.2 Given that everyone (PM, DV1, DV2, DV3, QAE) is not overworked, what is the probability of the product is not working and is released i.e., P(¬P,R | PM, DV1, DV2, DV3, QAE)? You cannot use a Bayesian Inference API to solve this (whether it was written by you or someone else). Please remember to round your answers as per the rounding rules of the exam (6 digits past decimal point)