Chebyshev Inequality Proof

Did you know that we can consider Chebyshev’s inequality a better version of the Empirical Rule? Why? Well, as we know, the Empirical rule tells us that

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$SOLVED:Use Chebyshev's inequality to show that if X and Y are two arbitrary random variables satisfying E{(X-Y)^2}=0, then we have P(X=Y)=1, namely X and Y are almost surely identical. [Hint: P(|X-Y|>ϵ)=0 for any ϵ>0 .]$

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