limiting relative frequency

More generally, empirical evidence, based on the results of many such repeatable experiments, indicates that any relative frequency of this sort will stabilize as the number of replications $n$ increases.

Definition

That is, as $n$ gets arbitrarily large, $n\left(A\right)/n$ approaches a limiting value referred to as the limiting (or long-run) relative frequency of the event $A$.

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The objective interpretation of probability identifies this limiting relative frequency with $P\left(A\right)$.

• Suppose that probabilities are assigned to events in accordance with their limiting relative frequencies. Then a statement such as “the probability of a package being delivered within one day of mailing is . 6 ” means that of a large number of mailed packages, roughly $60$ will arrive within one day.

• Similarly, if $B$ is the event that an appliance of a particular type will need service while under warranty, then $P\left(B\right)=.1$ is interpreted to mean that in the long run $10$ of such appliances will need warranty service.

• This doesn’t mean that exactly 1 out of 10 will need service, or that exactly 10 out of 100 will need service, because 10 and 100 are not the long run.

• objective relative frequency interpretation

• subjective relative frequency interpretation