Question

Explain the distribution function of a random variable

Answer 1

The discrete cumulative distribution function or distribution function of a real-valued discrete random variable X takes the countable number of points x₁, x₂, …. with corresponding probabilities p(x₁), p(x₂),… and then the cumulative distribution function is defined by
F_x(x) = P(X ≤ x), for all x ∈ R

i.e. F_x (x) = `sum_(x ≤ x) "P"(x_"i")`