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* [[Binomial distribution]], models the number of successes when someone draws n times with replacement. Each draw or experiment is independent, with two possible outcomes. The associated probability mass function is <math display="inline">\binom{n}{k}p^k (1-p)^{n-k}</math>. [[Image:Fair dice probability distribution.svg|right|thumb|The probability mass function of a [[Dice|fair die]]. All the numbers on the {{dice}} have an equal chance of appearing on top when the die stops rolling.]]{{pb}}An example of the binomial distribution is the probability of getting exactly one 6 when someone rolls a fair die three times.
* Geometric distribution describes the number of trials needed to get one success. Its probability mass function is <math display="inline">p_X(k) = (1-p)^{k-1} p</math>.{{pb}}An example is tossing the coin until the first head appears. The letter "p" denotes the probability of the head appears and "k" denotes the number of coin toss until the head appears. {{pb}}Other distributions that can be modeled using a probability mass function are the [[categorical distribution]] (also known as the generalized Bernoulli distribution) and the [[multinomial distribution]].
* If the discrete distribution has two or more categories one of which may occur, whether or not these categories have a natural ordering, when there is only a single trial (draw) this is a categorical distribution.
* An example of a [[Joint probability distribution|multivariate discrete distribution]], and of its probability mass function, is provided by the [[multinomial distribution]]. Here the multiple random variables are the numbers of successes in each of the categories after a given number of trials, and each non-zero probability mass gives the probability of a certain combination of numbers of successes in the various categories.
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