A Poisson process is a stochastic process that models the occurrence of events happening independently and at a constant average rate over time or space. It is widely used in fields such as telecommunications, finance, and natural sciences to describe random events like phone call arrivals, stock trades, or radioactive decay.

Poisson Process

Poisson process

A stochastic process is a collection of random variables representing the evolution of a system over time, where the future state depends on both the present state and inherent randomness. It is widely used in fields like finance, physics, and biology to model phenomena that evolve unpredictably over time.

stochastic process

occurrence of events

Independent events are two or more events in probability theory where the occurrence of one event does not affect the probability of the other event occurring. This means that the probability of both events happening is the product of their individual probabilities.

Independent Events

constant average rate

Telecommunications is the transmission of information over significant distances by electronic means, enabling communication between individuals, businesses, and governments across the globe. It encompasses a wide range of technologies, including telephones, radio, television, and the internet, playing a crucial role in modern society by facilitating instant communication and data exchange.

telecommunications

Finance is the science of managing money, including the processes of acquiring, investing, and utilizing funds to achieve personal, corporate, or governmental goals. It encompasses various activities such as budgeting, saving, lending, investing, and forecasting to optimize financial resources and ensure stability and growth.

finance

Natural sciences are branches of science that seek to understand the rules governing the natural world through empirical and scientific methods. They encompass disciplines that study the physical universe, from the subatomic to the cosmic scale, and include both observational and experimental approaches.

natural sciences

random events

phone call arrivals

stock trades

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation, leading to the transformation of the original atom into a different element or a different isotope of the same element. This process occurs spontaneously and is characterized by a specific half-life, which is the time it takes for half of the radioactive atoms in a sample to decay.

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