Question

Which of the following statements are true or false? Give reasons for your answers. By Chebyschev’s inequality, P{mode of x- my greater than equal to 2 sigma} smaller than equal to 0.2

Answer 1

Question #65581, Math / Statistics and Probability

Which of the following statements are true or false? Give reasons for your answers. By Chebyshev's inequality, $P\{\text{mode of } x\text{- my greater than equal to 2 sigma}\}$ smaller than equal to 0.2

Answer.

By the Chebyshev's inequality $P(|X - \mu| \geq k\sigma) \leq \frac{1}{k^2}$

So $P(|X - \mu| \geq 2\sigma) \leq \frac{1}{2^2} = \frac{1}{4} = 0.25 > 0.2$

Statement is False.

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