Follow the steps below to prove the LLN without using CLT.

(a) Let \(X\) be a random variable with mean \(\mu\) and variance \(\sigma^{2}\). Then for any real number \(\alpha>0, \operatorname{Pr}(|X-\mu| \geq \alpha) \leq \frac{\sigma^{2}}{\alpha^{2}}\).

(b) Apply Chebyshev's inequality to prove the LLN.