Problem 5 (10 marks) (a) A freelance computer network consultant, let's call her Yvonne, is employed in weekly contracts. Each week she is either: employed (E), unemployed (U) or training in new technology (T). Yvonne's records support the following assumptions: If she's employed this week, then next week she'll be employed with probability 0.80, and training in new technology with probability 0.05. If she's unemployed this week, then next week she'll be employed with probability 0.60 and training in new technology with probability 0.20. If she is training in new technology this week, then next week she'll be employed with proba- bility 0.70. She never trains in new technology for two consecutive weeks. We can model Yvonne's situation by a Markov process. Make a transition diagram to model Yvonne's situation. (b) A corporation, BIG CORP INDUSTRIES, seeks to understand which employees perform tasks that are the most important to the corporation's operation. Every employee has submitted a response to the following survey question: "List the names of colleagues whose work is important to yours." A PageRank-like approach' will be used to rank the importance of employees from this data. (i) Describe a directed graph (What is the set of vertices? When is there an edge from one vertex to another?) related to the survey data that may play the role of a 'webgraph' in a PageRank-like approach to ranking the importance of employees. (ii) State at least two hypotheses concerning the data and the importance of employees that, if assumed true, would justify the claim that a PageRank-like approach will be an effective way to rank the importance of employees. 14 (c) Let G be the webgraph with the adjacency matrix A shown below, and suppose that we are using the page rank algorithm with a damping factor of 80% (0.80) to rank the pages in G. A = 0110 1001 0 1 0 0 0000 (i) Draw a picture of G