Question

Differentiate between strong convergence of a random variable and weak convergence in probability

Answer 1

Solution:

For weak convergence law:

$\lim _{n \rightarrow \infty} P\left(\left|Y_{n}-Y\right|<\epsilon\right)=1$

For strong convergence law:

$P\left(\lim _{n \rightarrow \infty} \| Y_{n}-Y||<\epsilon\right)=1$