Transcript Simulation Presentation

Simulations as a Tool for
Reasoning About Probability and
Statistics
Revised from Presentation by Hollylynne S. Lee,
Tina T. Starling and Tyler Pulis
Karen Keene and Emily Thrasher
Today’s Objective: Focus on building
probability models and exploring behavior of
those models.
Real World
Collect Data
Inference about
Real World
If you collect data from the same context
or phenomena that you are interested in,
you are doing an EXPERIMENT
Real World Random Phenomena
Identify Assumptions
Choose Event of Interest
Build a Probability Model
Consider Possible Outcomes
Assign Probabilities
Design How to Simulate
Physical Device
Technology Tool
Simulate and Analyze Data
Make Inferences about Real World OR about Probability Model



Create explicit probabilistic models
Quickly replicate trials and store data
Represent and compare subsets of data,
both during and after a simulation
process
What do you think about this statement?
Does it make sense?
William: Well, in my family we have more boys; I have two brothers and one
sister.
Teacher: Does anyone have a family with more girls? [Several raise hands.]
Karen: In my family there are two of us: one boy, one girl.
Bruce: Well, I have two brothers, so we have three boys and no girls. Is that
considered “more boys”?
Linda: Sure, that makes sense. Three is more than zero.
Teacher: Yes, I agree with Linda, we should include all boys or all girls as being
“more.”
Kelly:
I bet a lot of families have equal boys and girls; isn’t it fifty-fifty to get a
boy or girl?
MaryBeth: I don’t know about that, my parents had five boys then me.
Talk to your neighbor
and come up with three
ways to model and
simulate a family of 4 kids
Try to name at least one
physical device and one
electronic tool you might
use.




Did anyone suggest 4 coin tosses as a way to
simulate a family of 4 children?
Why?
Need to unpack what a coin toss represents.
Assume probability of each gender is 50%
◦ this is a MODEL for what we think happens in the
real world…and it may be wrong!



Heads=Male, Tails=Female
We assume that a coin toss results in equal
chance of landing on heads on tails
Each coin toss represents a birth




Did anyone suggest choosing a random
number with something like a graphing
calculator or Excel?
Choose one of two numbers with equal
probabilities
Let’s Assign 1=Male and 0=Female
RandInt in calculator or Randbetween in
spreadsheet



Generate large sets of families of four
Use graphical representations to visualize the
frequency distributions as a means of making
sense of whether “most families” have more
boys or more girls in a large population.
This approach can develop a view of
probabilities as indicators of expectations
over many trials
Teacher: Tell me about the
graph. What does it tell you,
and how did it help you
think about the problem?
Kelly: This is a bar chart from
where we counted the
families for the number of
boys. It looks like a
mountain because most
families have two boys and
two girls. Each of the other
possibilities has less,
especially no boys or all
boys. So we think it is more
likely to have two boys and
two girls.

Tycho: What? That does not make sense to
me. Our group did the same thing, except we
created a different graph. I don’t understand
how your graph helps.


What did your simulation help you to
understand? Talk with a partner
How could you use simulations in your
classroom?