P(getting Pi correct to n digits after x trials)?

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SUMMARY

This discussion focuses on estimating the value of Pi using the Monte Carlo method and assessing the confidence in these estimates through statistical measures. The user highlights the importance of calculating the standard deviation from multiple trials to understand the margin of error in the approximation of Pi. Key resources provided include pseudo-code for variance and standard deviation calculations, as well as guidelines on the number of trials needed for accuracy. The discussion emphasizes the necessity of statistical analysis in validating Monte Carlo simulations.

PREREQUISITES
  • Understanding of the Monte Carlo method for numerical estimation
  • Familiarity with standard deviation and variance calculations
  • Knowledge of uniform distribution principles
  • Basic programming skills for implementing pseudo-code
NEXT STEPS
  • Research "Monte Carlo simulations in Python" for practical implementation
  • Learn about "confidence intervals in statistics" to enhance understanding of error margins
  • Study "variance and standard deviation formulas" for deeper statistical insight
  • Explore "sample size determination for statistical accuracy" to improve estimation reliability
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Mathematicians, statisticians, data scientists, and anyone interested in numerical methods for estimating constants like Pi through simulation techniques.

moonman239
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I would like to know how confident I can be in my Monte Carlo estimate of Pi, plus/minus a specified margin of error. I know the locations of the "pins" are uniformly distributed, thus P(pin being within circle's radius) = P(x <= radius) * P(y <= radius)
 
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Here are four links:

1) http://answers.yahoo.com/question/index?qid=20080107132917AAxtMth", Yahoo Answers
If you take N=100 dots you get an approximate value for pi, e.g. 3.241. Repeat this e.g. 20 times and have 20 approximate values for pi. For these 20 values you can calculate the standard deviation.

2) "www.evsis.org/docs/tdpp2_chap1.pdf"[/URL]
On page 4 to 6 of the document you will find a pseudo-code to calculate the variance and standard deviation.

3) [PLAIN]http://www.physics.sc.edu/~yar/phys309_2010/calculating_Pi/Pi_report.htm" )
This website talks about how many dots you need to ensure a certain number of correct digits.

4) http://mathforum.org/library/drmath/view/51909.html", Math Forum
This article discusses the standard deviation and confidence interval.
 
Last edited by a moderator:
I just gave myself a dopeslap for not thinking about using the standard deviation formula.
 

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