My libraryIn statistics, a univariate distribution is a probability distribution of only one random variable. Get More Information the world’s most comprehensive index of full-text books. This is in contrast to a multivariate distribution, the probability distribution Check This Out a random vector (consisting of multiple random variables). The univariate continuous uniform distribution on an interval [a, b] has the property that all sub-intervals of the same length are equally likely.
One of the simplest examples of a discrete univariate distribution is the discrete uniform distribution, where all elements of a finite set are equally likely. 1 At least 750 univariate discrete distributions have been reported in the literature.

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C is called a normalising constant

density core of f(x) can be called g

The pdf and cdf are related;
F(x) = \integral f(x)

The mean and variance are special cases of moments of distributions

the average, typical value of X

\mu = E(X) = \int_x_b

The mean is also known as the the first moment of a distribution
the second and third moments;
E(X^2) E(X^3)

central moments about the mean

@todo
Variance is the second central moment of a distribution
\mu_2

V(X) is the

a single formula for the moments of all r
the moment generating function mgf

@todo – Linearity of expectation is true only for finite sums?

Quantile function is the inverse of the cumulative distribution function
is written as X^2(v)

parameter is the degrees of you could try this out exponential distribution M(\lambda) is a special case of the X^2(v)
Student’s t distribution, t(v)

a special case of the t-distribution is the cauchy distribution with v=1

none of the moments of the Cauchy distribution exist, hence some of the general results such as the Central limit theorem do no apply. The distributions of continuous random variables are described by the probability distribution functions (pdfs) and cumulative distribution functions (cdfs)
should integrate to 1
non-negative
any mathematical function which is non-negative, positive on at least one interval of values of x, and has a finite integral can be made into a pdf. 2
Examples of commonly applied continuous univariate distributions3 include the normal distribution, Student’s t distribution, chisquare distribution, F distribution, exponential and gamma distributions. It is the probability model for the outcomes of tossing a fair coin, rolling a fair die, etc.

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Other examples of discrete univariate distributions include the binomial, geometric, negative binomial, and Poisson distributions.

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