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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?.

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Simulating Experiments

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  1. Simulating Experiments By: Justin Ross Tim Dietrich Brandon Izumi

  2. What is a Simulation? • A simulation is an imitation of chance behavior, based on a model that accurately reflects the experiment under consideration.

  3. 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 TI-83/89 or a computer, the problems become much easier and quicker to solve.

  4. Simulation Steps • State the problem or describe the experiment. • State the assumptions. • Assign digits to represent outcomes. • Simulate many repetitions. • State your conclusions.

  5. 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?

  6. 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.

  7. 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.

  8. 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.

  9. 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.

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