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A continuous distribution defined by the probability density function (PDF) $f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-(x-\mu)^2 / (2\sigma^2)}$ where $\mu$ is the mean and $\sigma$ is the standard deviation.

A special case of the Gamma distribution with $\alpha = k/2$ and $\theta = 2$, where $k$ is the degrees of freedom. The PDF is $f(x;k) = \frac{1}{2^{k/2}\Gamma(k/2)} x^{k/2-1}e^{-x/2}$ for $x > 0$.

A continuous distribution where all intervals of the same length within the distribution's range are equally probable. The PDF is $f(x) = \frac{1}{b-a}$ for $a \leq x \leq b$.

A discrete distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space when these events occur with a known constant mean rate ($\lambda$) and independently of the time since the last event. The PMF is $P(X = k) = \frac{e^{-\lambda} \lambda^k}{k!}$.

A discrete distribution that models the number of Bernoulli trials needed to get the first success. The PMF is $P(X = k) = (1-p)^{k-1}p$ for $k \geq 1$, where $p$ is the probability of success on each trial.

A continuous distribution defined on the interval [0, 1] and parameterized by two positive shape parameters, $\alpha$ and $\beta$. The PDF is $f(x;\alpha,\beta) = \frac{x^{\alpha-1}(1-x)^{\beta-1}}{B(\alpha, \beta)}$ where $B(\alpha, \beta)$ is the beta function.

A discrete distribution representing the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success ($p$). The probability mass function (PMF) is $P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}$ where $n$ is the number of trials and $k$ is the number of successes.

A continuous distribution that describes the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate. The PDF is $f(x;\lambda) = \lambda e^{-\lambda x}$ for $x \geq 0$.

A discrete distribution that describes the probability of $k$ successes in $n$ draws, without replacement, from a finite population of size $N$ that contains exactly $K$ successes. The PMF is $P(X = k) = \frac{{\binom{K}{k} \binom{N-K}{n-k}}}{{\binom{N}{n}}}$.