[triya]

Question Details:
Question Details:
Z


Alvie Singer lives at o in the accompanying diagram and has 4 friends who live at A, B,C, and D. One day Alvie decides to go visiting, so he tosses a fair coin twice to decide which of the four to visit. Once at a friend's house, he will either return home or else proceed to one of the adjacent houses( such as O, A or C when at B), with each of the three possibilities having probability 1/3. In this way, Alvie continues to visit friends until he returns home.

a) Let X= number of times that Alvie visits a friend. Derive the pmf of X.
b) Let Y= the number of straight line segments that Alvie transverses( including those leading to and frm 0). What is the pmf of Y.

[yingxiaodong]

p(z)=(24/54)(2/3)^(2z-2)