This example illustrates the long-run frequency interpretation of probabilities. We simulate the…

This example illustrates the long-run frequency interpretation of probabilities. We simulate the…
This example illustrates the long-run frequency interpretation of probabilities. We simulate the roll of a fair die on a computer. According to the definition of a fair die and the long-run frequency interpretation of probabilities, we should see that the percentage of times that any face appears should settle down near 100 6 % D 16:67% after many rolls. The word many cannot be quantified in general. The main point is that we should expect heterogeneity and oscillations in the percentages initially, but as we increase the number of rolls, the percentages should all approach 100 6 % D 16:67%. Here is a report of a computer simulation. Unmistakably, we see that the percentages appear to approach some limiting value when the number of rolls increases; indeed, they will all approach 16:67% when the number of rolls goes to infinity Apr 06 2022 11:33 AM