Question: 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

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.

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