Transcript Simulating Experiments

Simulating Experiments
By:
Justin Ross
Tim Dietrich
Brandon Izumi
What is a Simulation?
• A simulation is an imitation of chance
behavior, based on a model that
accurately reflects the experiment under
consideration.
Why use Simulations?
• It is much easier to simply use a model to
simulate a number of repetitions of the
experiment than to repeat the actual
experiment. You will save much time
with simulation; and with the aid of a TI83/89 or a computer, the problems
become much easier and quicker to solve.
Simulation Steps
1. State the problem or describe the
experiment.
2. State the assumptions.
3. Assign digits to represent outcomes.
4. Simulate many repetitions.
5. State your conclusions.
Step One
• State the problem or describe the
experiment.
– What is the likelihood that in a family of
four, there will be two girls and two boys?
Step Two
• State the assumptions.
– There is equal chance for having a boy or a
girl.
– Children are independent of each other;
meaning that the gender of one child will not
influence the gender of the next child.
Step Three
• Assign digits to represent outcomes.
– Table B will be used from the back of the
book, starting with line 101.
– Each digit in the table will represent a child
being born.
– Odd digits will represent girls; even digits
will represent boys.
Step Four
• Simulate many repetitions.
– For this I will use 30 families of four.
Digits – 1922 3950 3405 7562 8713
Sex
ffmm fffm fmmf ffmm mfff
2&2
Yes No Yes Yes No
25 additional repetitions were done making 30
total repetitions; 11 families had two boys and
two girls.
Step Five
• State your conclusions.
– I estimate that the probability of a family of
four having two boys and two girls being
11/30 or 37%. This may be inaccurate, do to
the fact that our simulation only had 30
repetitions. A calculator can easily be
programmed to do thousands of repetitions.