This study reveals for the first time the essential mechanism of tool-integrated reasoning through rigorous mathematical proof and develops a novel training algorithm that enables AI to utilize tools ...

This article was originally published at The Conversation. The publication contributed the article to Space.com's Expert Voices: Op-Ed & Insights I was preparing for my early morning class back in ...

I was preparing for my early morning class back in January 2025 when I received a notice regarding an asteroid called 2024 YR4. It said the probability it could hit Earth was unusually high. As ...

(The Conversation is an independent and nonprofit source of news, analysis and commentary from academic experts.) Toshi Hirabayashi, Georgia Institute of Technology (THE CONVERSATION) I was preparing ...

Add a description, image, and links to the bell-curve-probability-density-function topic page so that developers can more easily learn about it.

Once you have a basic understanding of sports betting odds, it’s easy to determine the favorite or underdog in a game and the favored option among a range of choices. You can also go a step further by ...

What Is A Probability Density Function? A probability density function, also known as a bell curve, is a fundamental statistics concept, that describes the likelihood of a continuous random variable ...

Abstract: A longstanding problem in statistics pertains to the estimation of probability density functions of continuous random variables from a finite set of their samples. In this paper, we propose ...