Top Qs
Timeline
Chat
Perspective

Probability vector

Vector with non-negative entries that add up to one From Wikipedia, the free encyclopedia

Remove ads

In mathematics and statistics, a probability vector or stochastic vector is a vector with non-negative entries that add up to one.

The positions (indices) of a probability vector represent the possible outcomes of a discrete random variable, and the vector gives us the probability mass function of that random variable, which is the standard way of characterizing a discrete probability distribution.[1]

Remove ads

Examples

Summarize
Perspective

Here are some examples of probability vectors. The vectors can be either columns or rows.

Remove ads

Geometric interpretation

Summarize
Perspective

Writing out the vector components of a vector as

the vector components must sum to one:

Each individual component must have a probability between zero and one:

for all . Therefore, the set of stochastic vectors coincides with the standard -simplex. It is a point if , a segment if , a (filled) triangle if , a (filled) tetrahedron if , etc.

Remove ads

Properties

  • The mean of the components of any probability vector is .
  • The shortest probability vector has the value as each component of the vector, and has a length of .
  • The longest probability vector has the value 1 in a single component and 0 in all others, and has a length of 1.
  • The shortest vector corresponds to maximum uncertainty, the longest to maximum certainty.
  • The length of a probability vector is equal to ; where is the variance of the elements of the probability vector.

See also

References

Loading content...
Loading related searches...

Wikiwand - on

Seamless Wikipedia browsing. On steroids.

Remove ads