Convergence concepts in probability MOC

Convergence in probability

A sequence (𝑋𝑖)∞𝑖=1 of real random variables is said to converge in probability to 𝑋 iff either of the equivalent conditions are met for all 𝜖 >0: prob

lim𝑖→∞ℙ(|𝑋𝑖−𝑋|>𝜖)=0lim𝑖→∞ℙ(|𝑋𝑖−𝑋|<𝜖)=1

This is precisely convergence under the Ky Fan metric.

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