Monte Carlo Simulation
Estimate quantities with random experiments.
Key idea
Estimate quantities with random experiments.
In depth
Estimate quantities by random sampling and averaging results. By the law of large numbers, accuracy improves like 1/√n. Useful when exact calculation is impractical.
Worked example
Estimate π: random points in a unit square; the fraction inside the quarter circle ≈ π/4.
Real-world uses
- Estimating risk in finance, project costs and the area of irregular shapes by random sampling
Common mistake
Using too few trials or a poor random generator.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Monte Carlo Simulation?
Estimate quantities with random experiments. It is a topic at the advanced level in Probability & Statistics.
Where is Monte Carlo Simulation used in real life?
Real-world examples: Estimating risk in finance, project costs and the area of irregular shapes by random sampling.
What should I learn before Monte Carlo Simulation?
Make sure you are comfortable with Bootstrap and Resampling, the previous topic in Probability & Statistics.
What is a common mistake with Monte Carlo Simulation?
Using too few trials or a poor random generator.
How can I practise Monte Carlo Simulation?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Monte Carlo Simulation?
Move on to Random Walks next.
Related advanced topics in Probability & Statistics
- Quartiles and IQR – Quartiles split data into four parts; IQR = Q3 − Q1.
- Box Plots – Five-number summary visualised.
- Outliers – Values beyond 1.5 IQR from the quartiles.
- Variance – Average squared deviation from the mean.
- Standard Deviation – Square root of variance; typical spread.
- Sample vs Population Variance – Divide by n−1 for sample variance.