Definition

A sequence of numbers X1,...,XnX_1,...,X_n converges in probability to a random variable XX, i.e. Xn →p XX_n \ \xrightarrow{p}\ X, if for all ϵ>0\epsilon>0,

limn→∞⁡P(|Xn−X|≥ϵ)=0\lim_{n \rightarrow \infty} P\big(|X_n-X| \geq \epsilon \big)=0

("Xn→XX_n \to X in probability")

See also

References

  1. https://www.probabilitycourse.com/chapter7/7_2_5_convergence_in_probability.php