Question

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 20. 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?

Answer 1

Roger's Theory- Diffusion of Innovation deals with the idea of how an innovation finds its space among the individual participants and the institutions as a whole. Roger proposes that Innovation needs four key 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 innovation. 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.