Distribution Convergence

Definition

For sequence of RV $X_1,X_2,\dots$ and RV $Y$ $X_n$ converges in probability to $Y$ if: ${\lim }_{n\to \infty }P(X_n\le x)=P(Y\le x),\forall x\in R$ (Denoted $X_n{\to }^{D}Y$)