Joint cumulative distribution function

The joint cumulative distribution function of a multivariate random variable $⃗ 𝐗 = (𝑋 𝑖) 𝑛 𝑖 = 1$ is #m/def/prob

𝐹 ⃗ 𝐗 (⃗ 𝐱) = ℙ (𝑛 ⋂ 𝑖 = 1 {𝑋 𝑖 \leq 𝑥 𝑖})

In order to find the cumulative distribution function of a single component $𝑋 𝑖$ of $⃗ 𝐗$ , called its marginal cumulative distribution function, one takes the limit of all other components

ℙ (𝑋 𝑖 \leq 𝑥 𝑖) = l i m 𝑥 𝑗 \to \infty, \forall 𝑗 \neq 𝑖 𝐹 ⃗ 𝐗 (⃗ 𝐱)

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