Spoke about the Markov Model
- there are multiple states
- path independence (history does not matter)

Look at the Files
Problems 151, 152 and 153

Q151. A cinema has a marquee with lots and lots of light bulbs. In any given week 1% of the light bulbs burn out. Unfortunately, between being busy and being sloppy, replacement is a little bit sporadic. Of all the bulbs that are burnt out, about 95% get replaced each week. Draw the state diagram for this system.

Q152. Translate this description into a state diagram. A population consists of people who play it safe, and daredevils. From year to year, most (97%) safe-players stay that way, but 2% turn into daredevils. About 1% of the safe-players die each year. By contrast, 10% of daredevils die each year and another 10%, seeing that, switch to playing it safe. All the other daredevils stick with the program.

Q153. A criminologist and an activist decide to collaborate on a project designed to reduce prison population. In the spirit of starting simple, they identify 4 states in which people can find themselves: never imprisoned; incarcerated; on parole; post-parole. The period of time in their analysis will be one year. Suppose 70% of the population has never been incarcerated. Each year 2% of these people are imprisoned. Of those currently incarcerated, 20% are released each year onto parole. Average parole is 5 years so that a person on parole has a 20% chance of finishing parole. Those on parole have a 10% chance of finding themselves back in prison in any given year. Individuals who are post parole have a 4% chance of returning to prison in any given year. Draw a state diagram and matrix representing this information.