What is Random

A big concept in statistics is randomness. Rolling a fair dice, or throwing a quarter, picking a sample from a population, sampling from some distribution. These behaviors all involved some randomness.

Very often, you can see a question like this: what's the probability of throwing a fair (50/50) quarter and you get heads? This is based on the assumption that throwing this quarter, this quarter will land randomly.

However, it is very tricky to think about this concept. Why would there be random? If you think really deep( not saying I can think deeper than you), every random behavior can be explained to be a deterministic behavior, and can be monitored and predicted, if, the power of computing is good enough, and power of measuring is accurate enough.

For example, throwing a quarter. There are many factors that involved with the quarter show head or tail after it land, such as: air flow speed, direction, landing angle, throwing angle, landing material, and so on. These things can all affect the result.

However, can we actually measure the air flow, throwing angle, and all these factors? This answer is quite difficult. Let's imagine that the air flow direction is the only factor affect result, the air is left and right.(which obviously is not the case), then when we throw quarter 100 times and 50 heads. It does not mean the coin itself is a fair coin, it can also be explained as the coin is not a fair coin, but the air flow direction somehow compensated the bias.

Therefore, I believe that in a reduced factor scenario, where there is no air and the quarter is dropped the same way many times, then every time the quarter should show the same side.

I believe it is very important to realize that everything in the world is in fact deterministic, we use probabilistic models is because there are so many factors that we have no idea how to capture. And remember "air flow direction" when you make a statement of a quarter's fairness.

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