Probability Convergence

Definition

For sequence of RV $X_1,X_2,\dots$ and RV $Y$ $X_n$ converges in probability to $Y$ if: ${\lim }_{n\to \infty }P(|X_n-Y|\ge ϵ)=0,\forall ϵ>0$ (Denoted $X_n{\to }^{P}Y$)