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 Two-State ...

Abstract: In this paper, we study three recently proposed probability mass function (PMF) estimation methods for flow cytometry data analysis. By modeling the PMFs as a mixture of simpler ...

The Upshot’s 2024 N.F.L. playoff simulator. See all teams Read the methodology, or select a team ALL TEAMS Arizona Cardinals Atlanta Falcons Baltimore Ravens Buffalo Bills Carolina Panthers Chicago ...

A function calculator is a powerful mathematical tool that helps students, engineers, and mathematicians alike determine if a given relation represents a function. As more individuals become aware of ...

A function is a mathematical expression that describes the relationship between two sets of values, typically input (x-values) and output (y-values). When the output value is zero, the corresponding ...

1 Department of Endocrinology, Beijing Tongren Hospital, Capital Medical University, Beijing, China 2 Beijing Tongren Hospital, Capital Medical University, Beijing, China Background: Previous findings ...

Abstract: Estimating the joint probability mass function (PMF) of a set of random variables from partially observed data is a crucial part of statistical learning and data analysis, with applications ...

New research reveals that the mass of newly born stars (yellow, orange, and red circles stand for stars from higher to lower mass) varies with their metal abundances and their birth time (inner circle ...