Question

2. One the last exam, you analyzed a mini-version of the board game Chutes and Ladders. For your reference, this information is repeated on the next page. (a) Give the one-step transition matrix P for the Markov chain {Xn,n 2 0]. (This is the same question that was on the exam) (b) What is the expected length (number of spins) of a game? (c) In which square should the player expect to spend the most time? (d) In which square should the player expect to spend the second-most amount of time? e) What is the probability that the player will ever land on square 11? (f) What is the probability that the player will ever land on square 2? (g) Given that the player is on square 8, what is the expected remaining length of the game? Consider a mini-version of the classic board game Chutes and Ladders, as shown in the picture below. A player starts with a token in square 1, and on each turn, spins a spinner to determine how many spaces to move (the spinner is equally likely to stop on 1, 2, or 3). If a player's move ends at the bottom of a ladder, he immediately climbs to the top of the ladder. If his move ends at the top of a chute, he immediately slides to the bottom of the chute. For example, if the player is currently on square 5 and he spins a 3, then his turn will end on square 8. If, however, he spins a 1, then his turn will end on square 9 10 12 Finish 7 6 5 1 Start2 4 3. In order to win the game, a player must land exactly on square 12. For example, if a player is on square 11 and spins a 2 or a 3, he will stay on square 11. He may only move from square 11 to square 12 by spinning a 1, Let represent the square that the player's token is on after the nth turn (so Xo = 1). Give the one-step transition matrix P for the Markov chain {Xn,n2 0

Answer 1

Roger's Theory-Diffusion of Innovation deals with the idea of how an innovation finds its space among the elements or participants to influence its spread among the stakeholders. The four elements are: 1. The Innovation itself: Anything that solves a human problem or reduces the effort to reach output from the input is called innovation. It can be process innovation, a service innovation or a product innovation. It is meant to reduce the effort to achieve an end result. 2. The Communication Channel: The medium of propagation of innovation is very crucial as information flow is very crucial for an innovation to propagate and increase participation and hence increase the life cycle of nnovation 3. Time: An innovation needs to pass the test of time. For a change to be accepted by all, take time and iterations. The telephone required participation from all adopters for the network to be successful and it took a fair amount of time. 4.Social System: Roger's suggests that external participants such as Mass media, government regulations and internal stakeholders' family, relationships etc. determine the social system and everyone must participate for innovations to flourish.