Abstract: This paper presents exact formulas for the probability distribution function (PDF) and moment generating function (MGF) of the sum-product of statistically independent but not necessarily ...

Modern physics relies on "Dark Energy," "Dark Matter," and over 20 arbitrary tuning parameters to explain the universe. A comprehensive AI-driven audit performed by Gemini Pro on 20 technical papers ...

Right now, molecules in the air are moving around you in chaotic and unpredictable ways. To make sense of such systems, physicists use a law known as the Boltzmann distribution, which, rather than ...

Follow ZDNET: Add us as a preferred source on Google. Linux is on the rise. I believe the popularity of the open-source operating system will continue to increase. Although Linux didn't reach the 10% ...

If mutual funds sold securities and realized gains, those gains need to be distributed to shareholders of record. Those distributions usually occur in November and December. It’s hard to estimate how ...

The international system has been ruptured. Russia’s invasion of Ukraine, gridlock at the un, growing American mercantilism and paralysis at the World Trade Organisation (WTO) have all contributed to ...

We collaborate with the world's leading lawyers to deliver news tailored for you. Sign Up for any (or all) of our 25+ Newsletters. Some states have laws and ethical rules regarding solicitation and ...

Interest Rate Probability Distributions Implied by Derivatives Prices is a daily measure of the distribution of future short-term interest rates, calculated from prices of fixed-income derivatives ...

Ask the publishers to restore access to 500,000+ books. An icon used to represent a menu that can be toggled by interacting with this icon. A line drawing of the Internet Archive headquarters building ...

The Langlands program has inspired and befuddled mathematicians for more than 50 years. A major advance has now opened up new worlds for them to explore One of the biggest stories in science has been ...

Breakthroughs, discoveries, and DIY tips sent six days a week. Terms of Service and Privacy Policy. Very little in this life is truly random. A coin flip is ...

Viewed creatively, the process for withdrawing required minimum distributions (RMDs) from an individual retirement account payable to a trust resembles a two-act play featuring “the twin pillars.” Act ...