The total area under the curve must equal 1, representing the fact that the probability of some outcome occurring within the entire range is certain. \[\int_{-\infty}^{\infty}f\left(x\right)dx=1\] ...

Abstract: An exact closed-form expression is developed for the probability density function (PDF) of the sum of independent but not necessarily identically ...

Abstract: An improved variable step size LMS algorithm based on logarithmic function is proposed. By improving the nonlinear-function relationship between the step ...

An illustration of a magnifying glass. An illustration of a magnifying glass.

A University of Alberta research team has uncovered a new role for a genetic mutation previously known to be linked to developmental disorders—and it could hold the key to more effective treatments ...

This volume first introduces the mathematical tools necessary for understanding and working with a broad class of applied stochastic models. The toolbox includes Gaussian processes, independently ...

It can be dangerous to go without sleeping, even for a day. Longer-term sleep deprivation can cause cognitive impairment, hallucinations, and other side effects. The longest recorded time without ...

Find all of Teen Vogue's questions and games stories here. We’ve all been there, staring down the silence of a conversation with no clear path. This is where a set of random questions to ask comes in ...

If you were one of the MacBook Air or MacBook Pro users who found MacOS Tahoe causing excessive battery drain and battery life reductions with MacOS 26.0 and MacOS 26.0.1, then you’ll want to update ...

Department of Chemistry, Department of Biomolecular Chemistry and National Center for Quantitative Biology of Complex Systems, University of Wisconsin—Madison, Madison, Wisconsin 53706, United States ...

LUBBOCK, Texas (KCBD) - As of October 1, 2025, citizens with alarm systems are now required to have a valid permit in compliance with the City of Lubbock’s updated False Alarm Ordinance. The Lubbock ...