Exercise $2$

Considier the Bayesian belief network below for the data set shown in Table $1.$

Table $1$ Data set

$\backslash$table$[[$Mileage$,$Engine,Air Conditioner,$\backslash$table$[[$Number of Records$],[$with Car Value$=$Hi$]],\backslash$table$[[$Number of Records$],[$with Car Value$=$Lo$]]],[$Hi$,$Good,Working,$3,4],[$Hi$,$Good,Broken,$1,2],[$Hi$,$Bad,Working,$1,5],[$Hi$,$Bad,Broken,$0,4],[$Lo$,$Good,Working,$9,0],[$Lo$,$Good,Broken,$5,1],[$Lo$,$Bad,Working,$1,2],[$Lo$,$Bad,Broken,$0,2]]$

a$)$ Given the network topology and the data set. Draw the CPT $($conditional probability table$)$ for all nodes.

b$)$ What is the probability that the Car Value will be high, if it has high Mileage, but bad engin and broken AirConditioner. Show all your calculations

c$)$ What is the probability of the engine being in good condition, given that the mileage is low, the car's value is low, but the air conditioner is in working order. Show all your calculations.