Consider a square (see below). In the center of the square lives Jes. His friends (four of them: Abe (A), Bagen(B), Calvin (C) and Danny (D)) each live at one of the four corners of the squares. Jes...

Consider a square (see below). In the center of the square lives Jes. His friends (four of them: Abe (A), Bagen(B), Calvin (C) and Danny (D)) each live at one of the four corners of the squares. Jes decides to visit a friend.
His choice is random and he is equally likely to visit any one of them first. Once at a friends house, he will either return home or else proceed to visit one of the nearest two adjacent friends. That is, if Jes is at D, then, he will
either return home or visit A or C, and the probability of each of the possibilities is the same. Following this pattern, Jes, continues to visit friends. Let X be the number of times Jes visits a friend (that is, the number of visits to friends).
(a) What is the pmf of X?
(b) What is the expected value of X?
(c) If we define a new random variable Y to be the number of straight line segments that Jes traverses, including those leading home. What is the pmf of Y ?