Let $Y_n\sim B(10, 2p) \wedge 0<p<\frac{1}{20}$.
prove or disprove:
$\lim_{n\rightarrow\infty}p(|Y_n-20p|>\epsilon) = 0$
my try:
$p(|Y_n-20p|>ϵ)=p(Y_n-20p>ϵ)+ p(Y_n-20p≤-ϵ) =p(Y_n>ϵ+20p)+p(Y_n≤20p-ϵ)= 1-p(Y_n≤ϵ+20p)+p(Y_n≤20p-ϵ)=$
But it goes complicated from here and I am not sure how to prove or disprove it.