Example package

Let $A$ be the event that a package sent within the state of California for $2^{\text{nd}}$ day delivery actually arrives within one day. The results from sending 10 such packages (the first 10 replications) are as follows:

Package #	1	2	3	4	5	6	7	8	9	10
Did A occur?	$\mathrm{N}$	Y	Y	Y	$\mathrm{N}$	$\mathrm{N}$	Y	Y	$\mathrm{N}$	N
Relative frequency of $A$	0	.5	.667	.75	.6	.5	.571	.625	.556	.5

Figure 2.2

Behavior of relative frequency (a) Initial fluctuation (b) Long-run stabilization

• Figure 2.2(a) shows how the relative frequency $n(A)/n$ fluctuates rather substantially over the course of the first 50 replications.
• But as the number of replications continues to increase, Figure 2.2(b) illustrates how the relative frequency stabilizes.

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