Random Hours

The other day I found myself somewhere where I usually am not, visiting in-laws, and wasting time going to the post office in order to send a watch back for warranty repair that did not work. On the way back my wife offered to take me to her hometown’s finest coffee spot which we learned was closed driving past. She apologized for the missed opportunity deriding the random hours of the shop. I’ve heard this particular description of a store’s hours more than a few times and figure that enough is enough. Beyond bemoaning the characterization I will in the next paragraphs describe what random hours would be.

What’s the big deal exactly? There is none, I just happen to wince at the concept of ‘random hours’ as a statistical industry worker and it seemed like something fun to write up. After all, it’s unlikely anyone actually means that the hours are actually random; they aren’t random to shop keeps and workers at the place that is open during somewhat unconventional times for some potential consumers. And if they never opened at times convenient to anyone they wouldn’t be open for very long anyway.

What could truly random hours look like? A shop keep could create an acceptable range of starting hours and then assign each to an integer. Using a random number generator on a computer, say Excel’s RANDBETWEEN() function, they would draw a uniformly distributed random number between the lowest and highest integers assigned to the starting hours. A uniformly distributed integer is a whole number that is drawn between the minimum and maximum of a group of numbers. These random draws are expected to be uniformly distributed, each of the numbers are equally likely to be drawn at any time, and as the number of draws grows larger each number is expected to be drawn an equal number of times. Once the shop keep had the random open time ready they could then perform a second random draw correlating to the number of minutes to be open. That would be random.

That’s a lot of drivel to debunk the idea that there are places that exist with owners who open at completely random hours. It won’t comfort those who can’t fathom the idea that they, as a bored out-of-town one time customer diverted off the main road isn’t exactly a lucrative customer base.