## Due Date: Due Wed May 28, 1:30pm in class or through the online dropbox. |

**A. [5pts]** Model this employment process as a Markov chain.

**B. [5pts]** If you start out employed, what is the probability of being employed at step three? Show all of your work.

**B. [5pts]** If you are unemployed at time 3, what is the probability that you started out employed at time 1

**C. [5pts]** What is the stationary distribution of the chain you defined?

**A. [14pts]** Model this problem as a Bayesian network representing a joint distribution over four binary random variables. Since there is more than one possible answer, briefly motivate your choices.

**B. [6pts]** Write three independence assumptions that your network encodes.

Consider the above Bayes net.

The variables are boolean and describe aspects of a court trail. They indicate whether someone broke an election law (**B**), was indicted (**I**), whether the prosecutor was politically motivated (**M**), if the person was found guilty (**G**), and if they were ultimately put in jail (**J**).

**A. [9pts]** Which of the following are true:

- P(B,I,M) = P(B) P(I) P(M)
- P(J|G) = P(J|G,I)
- P(M|G,B,I) = P(M|G,B,I,J)

**C. [3pts]** What is P(j,i,g | ¬m)?