Bernoulli and Uniform

Bernoulli vs. uniform distribution. The number of ways to distribute the brownies (assumed identical) is indeed $\dbinom{22}{2}$, by a standard "Stars and Bars" argument. However, these $\dbinom{22}{2}$ ways are not all equally likely.

source:
math.stackexchange.com

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slideplayer.com

Beta Distribution

Second, a consequence of the beta distribution being an exponential family is that it is the maximum entropy distribution for a set of sufficient statistics. In the beta distribution's case these statistics are $\log(x)$ and $\log(1-x)$ for $x$ in $[0,1]$. That means that if you only keep the average measurement of these sufficient statistics for a set of samples $x_1, \dots, x_n$, the minimum assumption you can make about the distribution of the samples is that it is beta-distributed.

source:
stats.stackexchange.com

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real-statistics.com

Binomial and Hypergeometric

Journal of Statistics Education, Volume 21, Number 1 (2013) 1 Distinguishing Between Binomial, Hypergeometric and Negative Binomial Distributions

source:
ww2.amstat.org

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youtube.com

Binomial Distribution

The binomial distribution is the basis for the popular binomial test of statistical significance. 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.

source:
en.wikipedia.org

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lookfordiagnosis.com

Construct a box Plot

The box plot (a.k.a. box and whisker diagram) is a standardized way of displaying the distribution of data based on the five number summary: minimum, first quartile, median, third quartile, and maximum.

source:
physics.csbsju.edu

Continuous Uniform Distribution

Uniform distribution (continuous) In probability theory and statistics, the continuous uniform distribution or rectangular distribution is a family of symmetric probability distributions such that for each member of the family, all intervals of the same length on the distribution's support are equally probable.

source:
en.wikipedia.org

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en.wikipedia.org

ConwayMaxwellPoisson Distribution

In probability theory and statistics, the Conway–Maxwell–Poisson (CMP or COM–Poisson) distribution is a discrete probability distribution named after Richard W. Conway, William L. Maxwell, and Siméon Denis Poisson that generalizes the Poisson distribution by adding a parameter to model overdispersion and underdispersion.

source:
en.wikipedia.org

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en.wikipedia.org

Degenerate Distribution

In mathematics, a degenerate distribution is a probability distribution in a space (discrete or continuous) with support only on a space of lower dimension. If the degenerate distribution is univariate (involving only a single random variable) it is a deterministic distribution and takes only a single value.

source:
en.wikipedia.org

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commons.wikimedia.org

Describe the Shape of a dot Plot

In this lesson you will learn about the shape of the distribution of data by looking at various graphs and observing symmetry, bell curves and skews.

source:
learnzillion.com

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cpalms.org

Exponential and Weibull

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source:
math.stackexchange.com

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itl.nist.gov

Gamma and Beta

This concerns the relationship between the Gamma and Beta distributions as opposed to the Gamma and Beta functions. Let $X \sim \mbox{Gamma}(\alpha, 1)$ and $Y \sim \mbox{Gamma}(\beta, 1)$ where the paramaterization is such that $\alpha$ is the shape parameter.

source:
math.stackexchange.com

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slideserve.com

Geometric and Negative Binomial

Geometric Distribution versus Negative Binomial Distribution. The geometric distribution describes the probability of "x trials are made before a success", and the negative binomial distribution describes that of "x trials are made before $r$ successes are obtained", where $r$ is fixed.

source:
math.stackexchange.com

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slideplayer.com

Kumaraswamy Distribution

Kumaraswamy distribution. In probability and statistics, the Kumaraswamy's double bounded distribution is a family of continuous probability distributions defined on the interval [0,1].

source:
en.wikipedia.org

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en.wikipedia.org

Normal, Log-Normal, Student's t, and Chi-Squared

Distributions related to the normal distribution Three important distributions: Chi-square (˜2) distribution. tdistribution. Fdistribution. Before we discuss the ˜2;t, and F distributions here are few important things about the gamma distribution. The gamma distribution is useful in modeling skewed distributions for variables that are not negative.

source:
stat.ucla.edu

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slideplayer.com

Poisson

The Poisson Distribution In the picture above are simultaneously portrayed several Poisson distributions. Where the rate of occurrence of some event, r (in this chart called lambda or l) is small, the range of likely possibilities will lie near the zero line.

source:
umass.edu

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keywordhungry.com

Skellam Distribution

The probability mass function for the Skellam distribution for a difference = − between two independent Poisson-distributed random variables with means and is given by: (;,) = {=} = − (+) / () where I k (z) is the modified Bessel function of the first kind.

source:
en.wikipedia.org

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sport12x.com