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 … [Continue reading]
In my last post, I introduced you to the so-called birthday problem. Namely, the probability of having at least one birthday coincidence in a random group of people. I showed you how to approach the question analytically by deriving a simple formula … [Continue reading]
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 … [Continue reading]
Welcome to my introductory post to a large series that I'm starting today. The main purpose of this post is to get you in the mood for the posts to follow. Namely, exploring and solving interesting probability questions from the real world. … [Continue reading]