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9.4
Simulation
P
urpose
The role this topic plays in quantitative reasoning
The modeling of random phenomenon needs the ability to simulate multiple iterations based upon a
set of input parameters. The weather models, stock market simulations, sports betting, and modeling
catastrophes all depend on multiple random variables. In fact, most cutting edge simulations require a
user to perform their own sampling of inputs and analysis of outputs. The skills associated with modeling
and simulation are valuable to future professionals and their presence in our everyday lives is always
increasing.
L
earning Goals
What you should learn while completing this activity
1. Understand how to use simulations to model a situation.
2. Learn the process for sampling from input distributions.
3. Use the output of simulations to explain the mathematics in the situation.
D
iscovery
Finding out for yourself
The chaos game illustrates how simulations can used to model randomness. In the game you start
with the three vertices of a triangle. Then a starting a random point inside the triangle, the next point
is halfway between the starting point and a randomly chosen vertex. The process is continued many
times, until the distribution of points is evident.
1. Before running the simulation, what distribution of points would you expect to get?
2. After running the simulation, what distribution of points did you get?
3. Why is it preferable to use a simulation for this game as opposed to performing the experiment
with paper and pencil?
W
hat Do You Already Know?
Tapping into your existing knowledge
1. What are probability distributions?
2. How are mathematical models affected by changes in the inputs?
3. How are inputs selected when modeling a situation?
M
athematical Language
Terms and notation
deterministic system
—
a deterministic system is a system in which no randomness is involved in
the development of future states of the system
iteration
—
one of many
repeated uses of a mathematical or computational model, each with static
inputs selected from a given distribution