SPM

1. Monte Carlo Simulations
by Gio
Other
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2. Basic Principle: Monte Carlo Method
• The Monte Carlo Method is the approach (methodology) of using
randomness to describe problems that may have a deterministic
solution
• The Law of Large Numbers (LLN) states that with an increase in the
number of measurements the expected value grows to equal the
average value
• A Pseudo-Random Number Generator is an algorithm for generating
numbers that appear reasonably random in sequence
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3. Law of Large Numbers
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4. Pseudo Random Number Generator
• Approximate randomness
• Probability distributions [0, 1]
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5. Monte Carlo Steps
• Step 1: Define the probability space and the points within that space; use a large number of points
to define the space
• Step 2: Define the conditions of the problem that constrains the space
• Step 3: Discriminate between the points that reside within the constraints of the problem and those
that do not
• Step 4: Use the points that reside within the constraints to define the space of the solution
• Important: The greater the number of points, the greater the accuracy of the simulation
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6. Colab Exercises
• Conditional Probability
• Basic Geometry
• Calculus
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7. Conditional Probability
• Which combination of numbers, on average, give a larger value; three
numbers between 1-4 or two number between 1-6? Always double
the lowest number in each combination.
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8. Basic Geometry
• Determine the area of basic geometric shapes without using the area
formulas for those shapes
• Relative areas
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9. Calculus
• Determine the area under the curve without integrating
• Random sampling
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10. Thank you!
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