An individual named Claudius is located at the point 0 in the accompanying diagram. Using an appropriate

Question:

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 first moves to one of the four locations B1, B2, B3, B4. Once at one of these locations, another randomization device is used to decide whether Claudius 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 umber of moves that Claudius makes before first 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).