4) Consider the DAG below for a Bayesian network which displays the relationship between a car's value (with values 'high' or 'low'), mileage (with values 'high' or 'low'), engine (with values 'good' or 'bad') and air conditioner (with values 'broken' or 'working'). Page 1 of 6 Mileage Air Engine Conditioner Car Value This Bayesian network is based on the following summarised data consisting of 40 observations, given in the table below. The number of observations with car value = high corresponding to all combinations of values for mileage, engine and air conditioner is given in the 4th column. Similarly, the number of observations with car value = low corresponding to all combinations of values of mileage, engine and air conditioner is given in the 5th column. Air Mileage Number of observations with Number of observations with Engine (E) conditioner (M) (AC) Car's value (CV) = High Car's value (CV) = Low High Good Working 3 4 High Good Broken 2 High Bad Working High Bad Broken Low Good Working Low Good Broken Low Bad Working 1 2 Low Bad Broken 0 2 Show all workings to determine the conditional probability tables (CPTS) on the next page for each of the nodes in the network. The probabilities in some of the CPTS have been done for you. Show all the necessary calculations, replicate the DAG and the set of CPTS in your answer book. [10] 9+5+1+0+0+1+2+2 20 4.1) 1 1 0 9 5 5 4 0 1 4) Consider the DAG below for a Bayesian network which displays the relationship between a car's value (with values 'high' or 'low'), mileage (with values 'high' or 'low'), engine (with values 'good' or 'bad') and air conditioner (with values 'broken' or 'working'). Page 1 of 6 Mileage Air Engine Conditioner Car Value This Bayesian network is based on the following summarised data consisting of 40 observations, given in the table below. The number of observations with car value = high corresponding to all combinations of values for mileage, engine and air conditioner is given in the 4th column. Similarly, the number of observations with car value = low corresponding to all combinations of values of mileage, engine and air conditioner is given in the 5th column. Air Mileage Number of observations with Number of observations with Engine (E) conditioner (M) (AC) Car's value (CV) = High Car's value (CV) = Low High Good Working 3 4 High Good Broken 2 High Bad Working High Bad Broken Low Good Working Low Good Broken Low Bad Working 1 2 Low Bad Broken 0 2 Show all workings to determine the conditional probability tables (CPTS) on the next page for each of the nodes in the network. The probabilities in some of the CPTS have been done for you. Show all the necessary calculations, replicate the DAG and the set of CPTS in your answer book. [10] 9+5+1+0+0+1+2+2 20 4.1) 1 1 0 9 5 5 4 0 1
