Joint probability mass function

The joint probability mass function $𝑓 ⃗ 𝐗$ of a discrete multivariate random variable $⃗ 𝐗 : 𝜉 \to ℝ 𝑛$ is #m/def/prob

𝑓 ⃗ 𝐗 (⃗ 𝐱) = ℙ (⃗ 𝐗 = ⃗ 𝐱)

In order to find the probability mass function of a single component $𝑋 𝑖$ of $⃗ 𝐗$ , called the marginal probability mass function, one can sum over all other components

ℙ (𝑋 𝑖 = 𝑦) = \sum ⃗ 𝐱 : 𝑥 𝑖 = 𝑦 𝑓 ⃗ 𝐗 (⃗ 𝐱)

#state/tidy | #lang/en | #SemBr