Midterm group 3

Flowcharts and Decision Models

aha!

Q71. Consider this little bit of logic that describes a tourist's thinking process (taken from the title of a 1970s movie): “if it’s Tuesday, this must be Belgium. Otherwise, I have no idea where we are.” Sketch a flowchart that represents this flow of thought.

hmm…

Q92. What is wrong with the decision tree here? I need to decide whether to work at home or go down to Stanford today. At home, because of distractions, I work at about 75% efficiency. If I go to my research office at Stanford I work at 100% efficiency. If I work at home I will get 8 hours to work. If I decide to drive down to Stanford, I will get 8 hours minus driving time to work. The normal drive is ^0 minutes each way. But about 20% of the time it is extra light and the round trip takes just 90 minutes. About 30% of the time, though, traffic is awful and round trip is 180 minutes. I made a decision tree to figure out where I should work if I am trying to maximize my output, but I did something wrong. Fix the tree and tell me what I should do.

decision-tree-problems-01.gif

uh-oh.

Q97. There's an idea in philosophy called "Pascal's Wager" that describes a way of thinking about the existence of god. It goes like this. I have a choice to believe or not believe. And there is a chance that god exists and a chance that there is no god. If I believe and there is a god, I have a chance at eternal salvation. If I don't believe but there is a god, I suffer eternal damnation. If I do believe and it turns out there is no god, I will feel a bit of a chump, but the atheists can feel smug if opposite is the case. Sketch this situation as a decision tree. Should you believe in god?


Difference Equations, Stock and Flow, and Feedback

aha!

Q112. Sketch a causal loop diagram representing this logic:
Being sad…

  1. …makes you frown…
  2. …which makes people avoid you…
  3. …which makes you lonely…
  4. …which makes you sad…

hmm…

Q111. Let's say we have a 2 year graduate program. The first year class is growing at a rapid rate 5% per year. Between the first and second years, 25% of the students change their minds or get jobs and leave the program. Among the second years, 10% leave before graduation. The program currently has 20 first year and 12 second year. Write difference equations to describe population in future years.

uh-oh.

Q132. Create both a causal loop and a stock and flow diagram for a thermostat, heater, and house. The house is a stock of air. When its temperature goes below some threshold, hot air is added. All along though, hot air is subtracted (or cold air is added) through leaky windows and the like. But the temperature does not change immediately upon introduction of the hot air. What are the challenges of modeling this phenomenon discretely and how can we solve them?


Markov Models

aha!

Q157. Sketch the transition matrix that corresponds to the following diagram

p0157-markov-01.jpg

hmm…

Q154. Suppose a given housing market has a 10% turnover rate each year. How many houses will typically be in the first, second, third, etc. year of their mortgage at any given time? Assume 10 year mortgages to keep things simple. Draw the diagram that would be the first step in solving this problem.

uh-oh.

Q158. Suppose the following statements are true about the local housing market.

  1. On a month to month basis, 90% of mortgage payments are on time, 10% are late or missed.
  2. Of all the late/missed payments, 25% are back on track the following month. 65% are late again. 10% go into default.
  3. Of all mortgages in default in a given month, 20% have a work-out and return to good standing. 70% remain in default and 10% move into foreclosure.
  4. Of all houses in foreclosure each month, the banks manage to get 20% back on the market and resold.

Draw the transition diagram and write out the transition matrix.


Actors and other Sorting and Peer Effects

aha!

Q166. Consider a one dimensional cellular automata that looks like this:
Generation 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0
Generation 2

Show what the next few generations would look like subject to "rule 93":

Rule 93
0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1
0 1 0 1 1 1 0 1

hmm…

Q172. Consider this data on the thresholds in a population. Draw a frequency histogram and cumulative frequency diagram. If news reports suggest participation will be at 20 people, how many people's threshold is met or exceeded? How about if the number is 70?

p0172-table-a.gif

uh-oh.

Q169. Consider the 12 block neighborhood bounded by parks on the north and south and major thoroughfares on the east and west. Green houses are supporting Obama, purple houses Romney.

p0169-segregation.gif

Using the facing blocks delineated by the red dashed lines as units (it yields 15 of them), calculate the index of dissimilarity.


Woohoo! Bonus question on Aggregation

Q167. Suppose we have a diffusion process in which all susceptibles who are in contact with an infected in a given time period become infected in the next time period. On the grids below color in squares to indicate what happens over the first six time periods beginning with one infected. Then fill in the table and chart the data.

p0167-grid.gif
p0167-table.gif
p0167-chart.gif