Last week I stumbled over Dimensional Analysis which is not only useful for applied fields (physics, biology, economics), but also for math (Why did no one tell me that you can almost always think of df/dx as having "the type of f"/"the type of x"? The fact that exponents always have to be unit-less etc.? It had never occurred to me to make this distinction. In my mind, f(x)=x went from the reals to the reals, just like _e^x_ did.

One example of a question that before I would have had to think slowly about:

Answer

The standard deviation has the unit of the random variable X, while the z-score is unitless _z=frac{X-mu}{sigma}_

If you found the above interesting, I recommend reading (or skimming) [...]

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