In today’s post I want to show you two alternative variance formulas to the main formula you’re used to seeing (both on this website and in other introductory texts).
Not only do these alternative formulas come in handy for the derivation of certain proofs and identities involving variance, they also further enrich our intuitive understanding of variance as a measure of dispersion for a finite population or a probability distribution.
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I have used the sum operator in many of my previous posts and I’m going to use it even more in the future. I’ve introduced bits and pieces about this notation and some of its properties but this information is scattered across many posts. For these reasons, I decided to dedicate a special post to the sum operator where I show you the most important details about it.
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Welcome to the third post from my series on numbers and arithmetic. In the previous two posts, I gave an overview of real numbers (and their main subsets), as well as the main operations between them. And in the rest of the series, we’re going to build all these concepts from scratch. Well, the focus in today’s post is the most basic subset of the real numbers: the natural numbers.
This post is part of my series Numbers, Arithmetic, and the Physical World.
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Welcome to the first post from my new series. Here we’re going look at a famous probability question often called the birthday problem. This is actually a more general question related to the probability of at least one coincidence after a fixed number of draws from a discrete uniform distribution.
This post is part of my series Probability Questions from the Real World.
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The topic of today’s post is mathematical functions. Functions are such a fundamental part of mathematics that you’re certain to encounter them almost everywhere.
Recently, I started a small series on numbers and arithmetic, in order to begin exploring the intuition of basic mathematical concepts that most of us take for granted. And these concepts themselves are the building blocks of more advanced concepts, including more advanced concepts in probability theory.
But to fully understand them, we also need to know the details and intuition of some general mathematical tools which we’re going to rely on along the way. Well, functions are first in line!
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Welcome to the second post from my series on numbers and arithmetic. As a sort of continuation to the introductory post, here I want to talk about the most important properties of arithmetic operations.
This post is part of my series Numbers, Arithmetic, and the Physical World.
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