Estimating sample size in monte carlo method
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estimate for the sample size N required to have the estimate of π within
[π − 0.01, π + 0.01] with 0.95 probability. and we are given nothing about the data except the fact that it is drawn from U ~ [-1,1]
I was thinking to apply this:
Necessary Sample Size = (Z-score)^2 * StdDev*(1-StdDev) / (margin of error)^2
but then we have to find stdDev for every N that will be too cumbersome.
can you help me out with this?
Edit:-
can we apply Central limit theorem?
statistics
asked Nov 10 at 19:14
Devkinandan Malav
11
add a comment |
up vote
0
down vote
favorite
estimate for the sample size N required to have the estimate of π within
[π − 0.01, π + 0.01] with 0.95 probability. and we are given nothing about the data except the fact that it is drawn from U ~ [-1,1]
I was thinking to apply this:
Necessary Sample Size = (Z-score)^2 * StdDev*(1-StdDev) / (margin of error)^2
but then we have to find stdDev for every N that will be too cumbersome.
can you help me out with this?
Edit:-
can we apply Central limit theorem?
statistics
asked Nov 10 at 19:14
Devkinandan Malav
11
Welcome to MathStackExchange, I think you may get what you need from Buffon's Needle, it's a classical problem that can derive a number related to $pi$. But please take a moment to check the FAQ on homework problems, I would suggest you edit your question to add some clarifications and context.
– Mefitico
Nov 10 at 19:27
thank you @Mefitico for the suggestion. but I am looking for sample size, not for the estimation of π. Buffon's Needle didn't serve my purpose.
– Devkinandan Malav
Nov 10 at 20:26
Note that the standard deviation you should use is that of the actual process, and not one inferred from the sample. Either you know something from the problem that allows you to compute $pi$ (which could be a trial with a known probability of success like $2/pi$). Or when that is not possible, you can pick the wort case deviation (=0.5).
– Mefitico
Nov 10 at 21:00
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
estimate for the sample size N required to have the estimate of π within
[π − 0.01, π + 0.01] with 0.95 probability. and we are given nothing about the data except the fact that it is drawn from U ~ [-1,1]
I was thinking to apply this:
Necessary Sample Size = (Z-score)^2 * StdDev*(1-StdDev) / (margin of error)^2
but then we have to find stdDev for every N that will be too cumbersome.
can you help me out with this?
Edit:-
can we apply Central limit theorem?
statistics
asked Nov 10 at 19:14
Devkinandan Malav
11
estimate for the sample size N required to have the estimate of π within
[π − 0.01, π + 0.01] with 0.95 probability. and we are given nothing about the data except the fact that it is drawn from U ~ [-1,1]
I was thinking to apply this:
Necessary Sample Size = (Z-score)^2 * StdDev*(1-StdDev) / (margin of error)^2
but then we have to find stdDev for every N that will be too cumbersome.
can you help me out with this?
Edit:-
can we apply Central limit theorem?
statistics
statistics
asked Nov 10 at 19:14
Devkinandan Malav
11
asked Nov 10 at 19:14
Devkinandan Malav
11
edited Nov 13 at 16:52
asked Nov 10 at 19:14
Devkinandan Malav
11
asked Nov 10 at 19:14
Devkinandan Malav
11
asked Nov 10 at 19:14
Devkinandan Malav
11
11
Welcome to MathStackExchange, I think you may get what you need from Buffon's Needle, it's a classical problem that can derive a number related to $pi$. But please take a moment to check the FAQ on homework problems, I would suggest you edit your question to add some clarifications and context.
– Mefitico
Nov 10 at 19:27
thank you @Mefitico for the suggestion. but I am looking for sample size, not for the estimation of π. Buffon's Needle didn't serve my purpose.
– Devkinandan Malav
Nov 10 at 20:26
Note that the standard deviation you should use is that of the actual process, and not one inferred from the sample. Either you know something from the problem that allows you to compute $pi$ (which could be a trial with a known probability of success like $2/pi$). Or when that is not possible, you can pick the wort case deviation (=0.5).
– Mefitico
Nov 10 at 21:00
add a comment |
Welcome to MathStackExchange, I think you may get what you need from Buffon's Needle, it's a classical problem that can derive a number related to $pi$. But please take a moment to check the FAQ on homework problems, I would suggest you edit your question to add some clarifications and context.
– Mefitico
Nov 10 at 19:27
thank you @Mefitico for the suggestion. but I am looking for sample size, not for the estimation of π. Buffon's Needle didn't serve my purpose.
– Devkinandan Malav
Nov 10 at 20:26
Note that the standard deviation you should use is that of the actual process, and not one inferred from the sample. Either you know something from the problem that allows you to compute $pi$ (which could be a trial with a known probability of success like $2/pi$). Or when that is not possible, you can pick the wort case deviation (=0.5).
– Mefitico
Nov 10 at 21:00
Welcome to MathStackExchange, I think you may get what you need from Buffon's Needle, it's a classical problem that can derive a number related to $pi$. But please take a moment to check the FAQ on homework problems, I would suggest you edit your question to add some clarifications and context.
– Mefitico
Nov 10 at 19:27
Welcome to MathStackExchange, I think you may get what you need from Buffon's Needle, it's a classical problem that can derive a number related to $pi$. But please take a moment to check the FAQ on homework problems, I would suggest you edit your question to add some clarifications and context.
– Mefitico
Nov 10 at 19:27
thank you @Mefitico for the suggestion. but I am looking for sample size, not for the estimation of π. Buffon's Needle didn't serve my purpose.
– Devkinandan Malav
Nov 10 at 20:26
thank you @Mefitico for the suggestion. but I am looking for sample size, not for the estimation of π. Buffon's Needle didn't serve my purpose.
– Devkinandan Malav
Nov 10 at 20:26
Note that the standard deviation you should use is that of the actual process, and not one inferred from the sample. Either you know something from the problem that allows you to compute $pi$ (which could be a trial with a known probability of success like $2/pi$). Or when that is not possible, you can pick the wort case deviation (=0.5).
– Mefitico
Nov 10 at 21:00
Note that the standard deviation you should use is that of the actual process, and not one inferred from the sample. Either you know something from the problem that allows you to compute $pi$ (which could be a trial with a known probability of success like $2/pi$). Or when that is not possible, you can pick the wort case deviation (=0.5).
– Mefitico
Nov 10 at 21:00
add a comment |
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Welcome to MathStackExchange, I think you may get what you need from Buffon's Needle, it's a classical problem that can derive a number related to $pi$. But please take a moment to check the FAQ on homework problems, I would suggest you edit your question to add some clarifications and context.
– Mefitico
Nov 10 at 19:27
thank you @Mefitico for the suggestion. but I am looking for sample size, not for the estimation of π. Buffon's Needle didn't serve my purpose.
– Devkinandan Malav
Nov 10 at 20:26
Note that the standard deviation you should use is that of the actual process, and not one inferred from the sample. Either you know something from the problem that allows you to compute $pi$ (which could be a trial with a known probability of success like $2/pi$). Or when that is not possible, you can pick the wort case deviation (=0.5).
– Mefitico
Nov 10 at 21:00