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Random Processes
Monte Carlo Simulation
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Random or Stochastic processes
Random or Stochastic processes
You cannot predict from the observation of one event,
how the next will come out
Examples:
Coin: the only prediction about outcome –
50% the coin will land on its tail
Dice: In large number of throws –
probability 1/6
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Question: What is the most probable number for
the sum of two dice?
12
11
10
9
8
7

6
11
10
9
8
7
6

5
10
9
8
7
6
5

4
9
8
7
6
5
4

3
8
7
6
5
4
3

2
7
6
5
4
3
2

1
6
5
4
3
2
1
36 possibilities
6 times – for
7
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Applications for MC simulation
Stochastic processes
Complex systems (science)
Numerical integration
Risk management
Financial planning
Cryptography
…
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How do we do that?
You let the computer to throw “the coin” and record
the outcome
You need a program that generates randomly a
variable
… with relevant probability distribution
Part 1
Random number generators
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