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Empirical Probability


The empirical probability of an event A in n repeated trials is the observed estimate of its probability, given by its relative frequency

 P^^_n(A)=1/nsum_(i=1)^n1_A(X_i)=(N_n(A))/n,

where N_n(A) is the number of trials in which A occurs and 1_A is the indicator function of A. If the trials are independent and identically distributed with probability P(A), the strong law of large numbers gives

 P^^_n(A)->P(A),

with probability 1 as n->infty.


See also

Probability, Relative Frequency, Strong Law of Large Numbers

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References

Ross, S. M. A First Course in Probability, 8th ed. Upper Saddle River, NJ: Pearson, 2010.

Cite this as:

Weisstein, Eric W. "Empirical Probability." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/EmpiricalProbability.html

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