$1.$ Bayesian network: Construction and basic understandings

$(15$ Marks$)$

In this problem you are asked to build a Bayesian network for the "life choices" domain. There's no right answer $($you can be creative$)$ but some networks will make much more sense than others. Here are the variables, each of which is boolean: StudyALot, GetGoodGrades, HaveHobbies, GoToGradSchool, GetGradDegree, GetJob, HaveFriends, GetMarried, HaveMoney, BeHappy.

a$.$ How many parameters does the full joint distribution for this domain have?

b$.$ Build a Bayesian network for this domain. You do not have to specify the Conditional Probability Distribution for each node.

c$.$ Write down the joint probability distribution in terms of the CPDs in your network.

d$.$ List $5$ important conditional independencies that are enforced by your network, and provide an informal justification for each one.

e$.$ How big is your Bayesian Network? How many independent parameters do the CPDs have?