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In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the ...
A discrete frequency domain is a frequency domain that is discrete rather than continuous. For example, the discrete Fourier transform maps a function having a discrete time domain into one having a discrete frequency domain. The discrete-time Fourier transform, on the other hand, maps functions with discrete time (discrete-time signals) to ...
Probability mass function is the probability distribution of a discrete random variable, and provides the possible values and their associated probabilities. It is the function defined by. The probabilities associated with all (hypothetical) values must be non-negative and sum up to 1, Thinking of probability as mass helps to avoid mistakes ...
Outline of discrete mathematics. Appearance. Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic [ 1 ] – do ...
In probability theory, the probability generating function of a discrete random variable is a power series representation (the generating function) of the probability mass function of the random variable. Probability generating functions are often employed for their succinct description of the sequence of probabilities Pr (X = i) in the ...
A continuity correction can also be applied when other discrete distributions supported on the integers are approximated by the normal distribution. For example, if X has a Poisson distribution with expected value λ then the variance of X is also λ, and. if Y is normally distributed with expectation and variance both λ.
The instantaneous rate of change is a well-defined concept that takes the ratio of the change in the dependent variable to the independent variable at a specific instant. This is an image of vials with different amounts of liquid. A continuous variable could be the volume of liquid in the vials. A discrete variable could be the number of vials.
The support of the Dirichlet distribution is the set of K -dimensional vectors whose entries are real numbers in the interval [0,1] such that , i.e. the sum of the coordinates is equal to 1. These can be viewed as the probabilities of a K -way categorical event. Another way to express this is that the domain of the Dirichlet distribution is ...