The Cauchy distribution’s counter-intuitive behavior

Someone with no exposure to probability or statistics likely has an intuitive sense that averaging random variables reduces variance, though they wouldn’t state it in those terms. They might, for example, agree that the average of several test grades gives a better assessment of a student than a single test

Arithmetic, Geometry, Harmony, and Gold

I recently ran across a theorem connecting the arithmetic mean, geometric mean, harmonic mean, and the golden ratio. Each of these comes fairly often, and there are elegant connections between them, but I don’t recall seeing all four together in one theorem before. Here’s the theorem [1]: The arithmetic, geometric,

Looking under the hood at the tech stack that powers multimodal AI

Ryan chats with Russ d’Sa, cofounder and CEO of LiveKit, about multimodal AI and the technology that makes it possible. They talk through the tech stack required, including the use of WebRTC and UDP protocols for real-time audio and video streaming. They also explore the big challenges involved in ensuring

Advice from CodeSignal CEO, Tigran Sloyan, on prepping for tech interviews & assessments

Taking a technical assessment is a common first step in the engineer hiring process—it allows employers to gain an early signal of candidate skill and gives applicants the opportunity to show off what they can do, regardless of their education or experience. Still, a coding assessment can be intimidating for

Building A 300 Channel Video Encoding Server

Discover how NETINT, Supermicro, and Ampere collaborated to build a groundbreaking 300 channel live stream video server. Continue reading Building A 300 Channel Video Encoding Server on SitePoint.

Ceva, cevians, and Routh’s theorem

I keep running into Edward John Routh (1831–1907). He is best known for the Routh-Hurwitz stability criterion but he pops up occasionally elsewhere. The previous post discussed Routh’s mnemonic for moments of inertia and his “stretch” theorem. This post will discuss his triangle theorem. Before stating Routh’s theorem, we need

Moments of inertia mnemonic

Edward John Routh (1831–1907) came up with a mnemonic for summarizing many formulas for moment of inertia of a solid rotating about an axis through its center of mass. Routh’s mnemonic is I = MS / k where M is the mass of an object, S is the sum of

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Binomial bound

I recently came across an upper bound I hadn’t seen before [1]. Given a binomial coefficient C(r, k), let n = min(k, r − k) and m = r −  n. Then for any ε > 0, C(n + m, n) ≤ (1 + ε)n + m / εn. The

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