The quality of AI-generated artifacts and answers improves when certificates are demanded, even if the evidence provided by ...

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 ...

The FIND function allows you to find a text string within another. It returns the position at which a character or string begins within another text string. The output of the above function will be 5, ...

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 ...

Abstract: This paper addresses models for time series of integer-valued variables. Such series arise in various applications, often as increment series for counts of interest. A model with a ...

Journal of Applied Probability, Vol. 58, No. 3 (SEPTEMBER 2021), pp. 621-636 (16 pages) Signatures are useful in analyzing and evaluating coherent systems. However, their computation is a challenging ...

Life is uncertain. None of us know what is going to happen. We know little of what has happened in the past or is happening now outside our immediate experience. Uncertainty has been called the ...

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 ...

Abstract: This paper presents an analysis of the average bit error probability (ABEP) based on the moment generating function (MGF) over the Beaulieu-Xie fading ...

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 ...

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 ...