9. An individual named Claudius is located at the point 0 in the accompanying diagram.

Using an appropriate randomization device (such as a tetrahedral die, one having four sides), Claudius rst moves to one of the four locations B1, B2, B3, B4.

Once at one of these locations, he uses another randomization device to decide whether he next returns to 0 or next visits one of the other two adjacent points. This process then continues; after each move, another move to one of the (new) adjacent points is determined by tossing an appropriate die or coin.

a. Let X  the number of moves that Claudius makes before rst returning to 0. What are possible values of X? Is X discrete or continuous?

b. If moves are allowed also along the diagonal paths connecting 0 to A1, A2, A3, and A4, respectively, answer the questions in part (a).