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Boltzmann's distribution is an exponential distribution. Boltzmann factor (vertical axis) as a function of temperature T for several energy differences ε i − ε j.. In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution [1]) is a probability distribution or probability measure that gives the probability that a system will be in a certain ...
The density of states related to volume V and N countable energy levels is defined as: = = (()). Because the smallest allowed change of momentum for a particle in a box of dimension and length is () = (/), the volume-related density of states for continuous energy levels is obtained in the limit as ():= (()), Here, is the spatial dimension of the considered system and the wave vector.
In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time if these events occur with a known constant mean rate and independently of the time since the last event. [1]
Given two random variables that are defined on the same probability space, [1] the joint probability distribution is the corresponding probability distribution on all possible pairs of outputs.
Population density is defined as the population divided by land area. Data are from the US Census unless otherwise specified. Population data are for the year 2023 [2] and area data are for the year 2010. [3] Some population estimates for territories are from the United Nations Commission on Population and Development. [4]
Drainage density is a quantity used to describe physical parameters of a drainage basin. First described by Robert E. Horton, drainage density is defined as the total length of channel in a drainage basin divided by the total area, represented by the following equation:
The binomial distribution is frequently used to model the number of successes in a sample of size n drawn with replacement from a population of size N. If the sampling is carried out without replacement, the draws are not independent and so the resulting distribution is a hypergeometric distribution , not a binomial one.
In 2023, Canada's population jumped by over 1 million people for the first time in the country's history. The population now stands at 39.5 million and is set to pass the 40 million mark later this year. The population growth has largely been fuelled by migrants who have been brought into the country to ease labour shortages. [55]