Bad grammar

I don't have that much longer to finish my catalog of named results for the Q (not to mention that I need to actually study these results, not just write about them). However, I'm going to burn another day's post with a comment about notation. It comes from a generalization of Chebychev's Inequality.

Since it's a named result (though not one I've found much use for), I'll start by stating it in it's usual form:

If X is a random variable from a distribution with mean μ and variance σ², then P(|X ‑ μ| ≥ kσ) ≤ k^‑2.

OK, great. Now consider a random sample from the same distribution: X₁, ..., X_n. Suppose we don't know what μ and σ² are. What can we say about the bound using just the sample mean and standard deviation? Well, get ready...



So far, just another messy formula but, it gets better. What's g?



Ummm, OK, you have a function of t and the answer in terms of ν and a. Oh, yeah, don't stress about that; they're both functions of t:



Oh, that's right, they're also a functions of n WHICH ISN'T ANYWHERE TO BE FOUND IN THE PARAMETER LIST. That's nuts. I'm not going to spend a lot of time trying to come up with a better way to express a result that I don't care about, but there simply has to be something better than that.