Convergence in distribution

A sequence $(𝑋 𝑖) \infty 𝑖 = 1$ of real random variables is said to converge in distribution to a real random variable $𝑋$ iff the CDFs obey prob

l i m 𝑖 \to \infty 𝐹 𝑋 𝑖 (𝑥) = 𝐹 𝑋 (𝑥)

for all points where $𝐹 𝑋 (𝑥)$ is continuous.