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Q
uantitative
R
easoning &
P
roblem
S
olving
438
© 2014 Pacific Crest
simulation
—
the repeated modeling of the operation of a real-world process or system with inputs
randomly taken from distributions rather than constants
stochastic modeling
—
a tool for estimating probability distributions of potential outcomes by
allowing for random variation in one or more inputs over time. The random variation is usually
based on fluctuations observed in historical data for a selected period using standard time-series
techniques.
I
nformation
What you need to know
R
eadings
R
esources
M
ethodology
U
sing a
S
imulation
Scenario:
What is the probability of having two girls in a family with three children?
Step
Explanation
Watch it Work!
1.
Do you need a
simulation?
Identify the situation you want
to model. Can you use an
experiment?
The situation is easily modeled.
A controlled experiment is not
practical.
2.
Choose the probability
distributions for the
input(s)
What distribution best models
the input of the model?
Initially we will use a uniform
distribution with equal probabilities
for a boy or girl with each child.
3.
How do you sample the
inputs?
Determine a way of providing
inputs for the simulation that
correspond to the probabilities
from step 2.
We will use a random number
generator to choose either 0 or 1.
We will let 0 represent a boy and 1
represent a girl.
4.
Run the simulation
Run the model enough times
to properly sample the input
distribution and reveal a stable
pattern.
We will simulate 10000 families
with 3 children several times and
see the probability of having two
girls to be about 0.38
5.
What is the distribution of
the output?
What distribution best models
the output of the model?
The number of girls in each family
results in a symmetric binomial
distribution. The probability of
having two girls is about 0.375
6.
Vary the input distribution
and repeat steps 4 and 5
Experiment with other
distributions for the input
to see how this affects the
output.
Increasing or decreasing the
probability of having a girl results
in a skewed binomial distribution
7.
What is the overall pattern
of the outputs?
Does step 6 change the
results of the simulation? Why
or why not?
The results were skewed since it
was more or less likely to have a
girl with each child. The pattern is
always a binomial distribution.
8.
Validate the results
Compare the results of the
simulation with real data
Comparing with actual data we
find agreement.