Consider the "cad1" data set in the package gRbase. There are 236 observations on fourteen variables from the Danish Heart Clinic. Suppose that a structural learning algorithm, together with prior knowledge, has identified the following network as "optimal". Coronary Artery Disease [sex] Sex Smoker SuffHearth Inherit Hyper chol CAD a) Construct the above network in R, and infer the Conditional Probability Tables (local distributions) from the data. **Hint-look into the function "xtable", it will help! Next, identify any d-seperations in the graph. b) Suppose it is known that a new female is observed to have hypercholestermia (high cholesterol). Absorb the evidence into the graph and revise the probabilities. How does the probability of Heart Failure and Coronary Artery Disease (CAD) change after this information is considered? c) Simulate a new dataset with 15 observations conditional upon this new information. Present this new data in a table form. Using this new dataset and the "predict" function, I want you to estimate the probability of "Smoker" and "CAD" given the other variables in your model. Consider the "cad1" data set in the package gRbase. There are 236 observations on fourteen variables from the Danish Heart Clinic. Suppose that a structural learning algorithm, together with prior knowledge, has identified the following network as "optimal". Coronary Artery Disease [sex] Sex Smoker SuffHearth Inherit Hyper chol CAD a) Construct the above network in R, and infer the Conditional Probability Tables (local distributions) from the data. **Hint-look into the function "xtable", it will help! Next, identify any d-seperations in the graph. b) Suppose it is known that a new female is observed to have hypercholestermia (high cholesterol). Absorb the evidence into the graph and revise the probabilities. How does the probability of Heart Failure and Coronary Artery Disease (CAD) change after this information is considered? c) Simulate a new dataset with 15 observations conditional upon this new information. Present this new data in a table form. Using this new dataset and the "predict" function, I want you to estimate the probability of "Smoker" and "CAD" given the other variables in your model