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chance.pdf

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chance.pdf

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Chance, Choice, and Change

Can Random Events Follow Laws?

ISC1057

Janet Peterson and John Burkardt

Computational Thinking

Fall Semester 2016

1 / 104

In this section of the course, we will look at things that seem to

have an element of chance or randomness.

We will try to understand how randomness can be created,

understood, and measured.

We will look at common instances of randomness, especially games

of chance.

We will talk about measuring the kinds of randomness, and how it

is possible for a computer to simulate random behaviors.

2 / 104

3 / 104

In 1946, Stanlislaw Ulam was a physicist working at Los Alamos,

trying to predict the behavior of a beam of neutrons that penetrate

a material.

If a neutron collides with an atom in the material, it can be

absorbed, be deﬂected at a new angle and speed, or cause the

atom to split.

For one neutron and one collision, Ulam could estimate the

probability of each event. The problem was that a single neutron

might cause many collisions, with the outcome diﬀerent each time.

Getting a useful answer meant estimating the behavior of many

neutrons and many collisions, which seemed impossible to

calculate.

4 / 104

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