We'll also see how well it generates new data, and finally we'll go over the key limitations of the copilot function. At the very end, I'll show you an alternative function to the copilot formula in ...

ABSTRACT: We obtain an infinite series expression for the joint probability density function of occupation times in a Three-State Markov chain. By extending the identity given by Darroch, we ...

ABSTRACT: We obtain a closed form expression for the joint probability mass function of the occupation times for a Three-State Markov chain. Our representation extends the long-standing result for a ...

Physics and Python stuff. Most of the videos here are either adapted from class lectures or solving physics problems. I really like to use numerical calculations without all the fancy programming ...

Function raises $10M led by Galaxy Digital to help institutions earn yield on bitcoin using FBTC, a fully backed, custody-safe DeFi product. Function, a crypto infrastructure startup, has raised $10 ...

As is well known, the normal distribution is a key tool in probability and statistics. It can be described as a distribution that obeys a universal rule derived from one of the most important theorems ...

Function-calling agent models, a significant advancement within large language models (LLMs), face the challenge of requiring high-quality, diverse, and verifiable datasets. These models interpret ...

Abstract: In this work, we propose two information generating functions: general weighted information and relative information generating functions, and study their properties. It is shown that the ...

Java is an object-oriented programming language. To create objects and meaningfully initialize them, a developer must use a Java constructor. Constructors are a critical part of software development ...

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 ...