Probability mass function: Difference between revisions

Revision as of 08:12, 13 October 2024

Revision as of 23:08, 26 December 2024

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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 {{dice}}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.