I'm having trouble with the following inequality, I am not sure whether it is correct:
$$ P((X_n-X)^2+(Y_n-Y)^2>\epsilon^2) \stackrel{?}{\le} P(|X_n-X|>\epsilon)+P(|Y_n-Y|>\epsilon) $$
I'm having trouble with the following inequality, I am not sure whether it is correct:
$$ P((X_n-X)^2+(Y_n-Y)^2>\epsilon^2) \stackrel{?}{\le} P(|X_n-X|>\epsilon)+P(|Y_n-Y|>\epsilon) $$