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Jul 1, 2022 at 17:53 comment added Robert Israel Chebyshev's inequality says $$\mathbb P\left(|X_n - \mu_n| \ge k_n \sigma_n\right) \le \frac{1}{k_n^2}$$ so $$\mathbb P\left(X_n > \mu_n - k_n \sigma_n\right) \ge 1 - \mathbb P\left(|X_n - \mu_n| \ge k_n \sigma_n\right) \ge 1 - \frac{1}{k_n^2}$$
Jun 30, 2022 at 12:17 comment added Scriddie How exactly are you using Chebyshev's inequality here?
Feb 4, 2016 at 22:35 history edited Robert Israel CC BY-SA 3.0
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Feb 4, 2016 at 22:25 history answered Robert Israel CC BY-SA 3.0