Editing Probability mass function (section)

==Examples==
{{Main|Bernoulli distribution|Binomial distribution|Geometric distribution}}

===Finite===
There are three major distributions associated, the [[Bernoulli distribution]], the [[binomial distribution]] and the [[geometric distribution]].

*Bernoulli distribution: '''ber(p) ''', is used to model an experiment with only two possible outcomes. The two outcomes are often encoded as 1 and 0. <math display="block">p_X(x) = \begin{cases}
p, & \text{if }x\text{ is 1} \\
1-p, & \text{if }x\text{ is 0}
\end{cases}</math> An example of the Bernoulli distribution is tossing a coin. Suppose that <math>S</math> is the sample space of all outcomes of a single toss of a [[fair coin]], and <math>X</math> is the random variable defined on <math>S</math> assigning 0 to the category "tails" and 1 to the category "heads".  Since the coin is fair, the probability mass function is <math display="block">p_X(x) = \begin{cases}
\frac{1}{2}, &x = 0,\\
\frac{1}{2}, &x = 1,\\
0, &x \notin \{0, 1\}.
\end{cases}</math>
* 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 die 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 a coin until the first "heads" appears. <math>p</math> denotes the probability of the outcome "heads", and <math>k</math> denotes the number of necessary coin tosses. {{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.
{{clear}}

===Infinite===
The following exponentially declining distribution is an example of a distribution with an infinite number of possible outcomes—all the positive integers: <math display="block">\text{Pr}(X=i)= \frac{1}{2^i}\qquad \text{for } i=1, 2, 3, \dots </math> Despite the infinite number of possible outcomes, the total probability mass is 1/2 + 1/4 + 1/8 + ⋯ = 1, satisfying the unit total probability requirement for a probability distribution.