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

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In summary, the conversation discusses using a Monte Carlo estimate to calculate the value of Pi with a specified margin of error. The method involves taking a certain number of dots and repeating the process multiple times to calculate the standard deviation. The conversation also references a document that provides a pseudo-code for calculating the variance and standard deviation, as well as a website that discusses the number of dots needed for a certain level of accuracy. Finally, an article is mentioned that discusses the standard deviation and confidence interval.
  • #1
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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  • #2
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.
 
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  • #3
I just gave myself a dopeslap for not thinking about using the standard deviation formula.
 

What is the probability of getting Pi correct to n digits after x trials?

The probability of getting Pi correct to n digits after x trials depends on the method used to calculate Pi, the accuracy of the calculations, and the number of trials performed. It is difficult to provide a specific probability without these details.

Is there a specific formula or method for calculating the probability of getting Pi correct to n digits after x trials?

There is no specific formula or method for calculating the probability of getting Pi correct to n digits after x trials. It is a complex mathematical problem that requires advanced techniques such as Monte Carlo simulations.

How many trials are needed to get Pi correct to n digits with a certain probability?

The number of trials needed to get Pi correct to n digits with a certain probability varies depending on the desired accuracy and the method used to calculate Pi. Generally, the more trials performed, the higher the probability of getting Pi correct to n digits.

Can the probability of getting Pi correct to n digits after x trials be increased?

The probability of getting Pi correct to n digits after x trials can be increased by increasing the number of trials or using more accurate methods for calculating Pi. However, it is impossible to achieve a 100% probability.

How does the accuracy of the calculations affect the probability of getting Pi correct to n digits after x trials?

The accuracy of the calculations has a direct impact on the probability of getting Pi correct to n digits after x trials. The more accurate the calculations, the higher the probability of getting Pi correct to n digits. However, achieving a high level of accuracy can be challenging and time-consuming.

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