Please provide steps for how you got the solution to the problem provided below. A freelance worker spends her days doing one of two things: working on a project or looking for a new project. Whenever she has a project to work on, she dedicates her full attention to it. On a particular month, she will complete the current project with probability 0.3. After completing project she takes the rest of the month off, and then at the beginning of the next month starts looking for work. On a given month, she will successfully find a new project with probability 0.85. After identifying a new project, she will start working on it at the beginning of the next month. i. Model the status of the worker (looking for a project of busy working a project) as a Markov chain. Give transition matrix. ii. Suppose that on March 1st she started looking for a new project. Find the probability that she will be working on a project during the month of May.
Please provide steps for how you got the solution to the problem provided below.
A freelance worker spends her days doing one of two things: working on a project or looking for a new project. Whenever she has a project to work on, she dedicates her full attention to it. On a particular month, she will complete the current project with probability 0.3. After completing project she takes the rest of the month off, and then at the beginning of the next month starts looking for work. On a given month, she will successfully find a new project with probability 0.85. After identifying a new project, she will start working on it at the beginning of the next month.
i. Model the status of the worker (looking for a project of busy working a project) as a Markov chain. Give transition matrix.
ii. Suppose that on March 1st she started looking for a new project. Find the probability that she will be working on a project during the month of May.
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