Estimator of True Probability
|The best estimator for the actual value is the estimator .
This estimator has a margin of error (E) where at a particular confidence level.
Using this approach, to decide the number of times the coin should be tossed, two parameters are required:
- The confidence level which is denoted by confidence interval (Z)
- The maximum (acceptable) error (E)
- The confidence level is denoted by Z and is given by the Z-value of a standard normal distribution. This value can be read off a standard score statistics table for the normal distribution. Some examples are:
|Z value||Confidence Level||Comment|
|0.6745||gives 50.000% level of confidence||Half|
|1.0000||gives 68.269% level of confidence||One std dev|
|1.6449||gives 90.000% level of confidence||"One Nine"|
|1.9599||gives 95.000% level of confidence||95 percent|
|2.0000||gives 95.450% level of confidence||Two std dev|
|2.5759||gives 99.000% level of confidence||"Two Nines"|
|3.0000||gives 99.730% level of confidence||Three std dev|
|3.2905||gives 99.900% level of confidence||"Three Nines"|
|3.8906||gives 99.990% level of confidence||"Four Nines"|
|4.0000||gives 99.993% level of confidence||Four std dev|
|4.4172||gives 99.999% level of confidence||"Five Nines"|
- The maximum error (E) is defined by where is the estimated probability of obtaining heads. Note: is the same actual probability (of obtaining heads) as of the previous section in this article.
- In statistics, the estimate of a proportion of a sample (denoted by p) has a standard error (standard deviation of error) given by:
where n is the number of trials (which was denoted by N in the previous paragraph).
This standard error function of p has a maximum at . Further, in the case of a coin being tossed, it is likely that p will be not far from 0.5, so it is reasonable to take p=0.5 in the following:
And hence the value of maximum error (E) is given by
Solving for the required number of coin tosses, n,
Read more about this topic: Checking Whether A Coin Is Fair
Famous quotes containing the words true and/or probability:
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—Gustave Flaubert (18211880)
“Crushed to earth and rising again is an authors gymnastic. Once he fails to struggle to his feet and grab his pen, he will contemplate a fact he should never permit himself to face: that in all probability books have been written, are being written, will be written, better than anything he has done, is doing, or will do.”
—Fannie Hurst (18891968)