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Problem 2

Problem statement: Let $ X $ be a continuous or discrete random variable with mean $ \mu $ and variance $ \sigma^2 $. Then, $ \forall \varepsilon >0 $, we have
$ P(|X-\mu| \geq \varepsilon) \leq \frac{\sigma^2}{\varepsilon^2} $

$ \color{blue}\text{Solution 1:} $

$ \color{blue}\text{Solution 2:} $

Discrete Case:
Continuous Case: