Probability vector

Examples

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

• ${\displaystyle x_{0}={\begin{bmatrix}0.5\\0.25\\0.25\end{bmatrix}},}$
• ${\displaystyle x_{1}={\begin{bmatrix}0\\1\\0\end{bmatrix}},}$
• ${\displaystyle x_{2}={\begin{bmatrix}0.65&0.35\end{bmatrix}},}$
• ${\displaystyle x_{3}={\begin{bmatrix}0.3&0.5&0.07&0.1&0.03\end{bmatrix}}.}$

Geometric interpretation

Writing out the vector components of a vector ${\displaystyle p}$ as

${\displaystyle p={\begin{bmatrix}p_{1}\\p_{2}\\\vdots \\p_{n}\end{bmatrix}}\quad {\text{or}}\quad p={\begin{bmatrix}p_{1}&p_{2}&\cdots &p_{n}\end{bmatrix}}}$

the vector components must sum to one:

${\displaystyle \sum _{i=1}^{n}p_{i}=1}$

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

${\displaystyle 0\leq p_{i}\leq 1}$