(Requires Appendix material)This question requires you to work with Chebychev's Inequality.
(a)State Chebychev's Inequality.
(b)Chebychev's Inequality is sometimes stated in the form "The probability that a random variable is further than k standard deviations from its mean is less than 1/k²." Deduce this form. (Hint: choose ? artfully.)
(c)If X is distributed N(0,1), what is the probability that X is two standard deviations from its mean? Three? What is the Chebychev bound for these values?
(d)It is sometimes said that the Chebychev inequality is not "sharp." What does that mean?

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The Answer of (Requires Appendix material)This question requires you to work with Chebychev's Inequality. (a)State Chebychev's Inequality. (b)Chebychev's Inequality is sometimes stated in the form "The probability that a random variable is further than k standard deviations from its mean is less than 1/k²." Deduce this form. (Hint: choose ? artfully.) (c)If X is distributed N(0,1), what is the probability that X is two standard deviations from its mean? Three? What is the Chebychev bound for these values? (d)It is sometimes said that the Chebychev inequality is not "sharp." What does that mean?

(Requires Appendix Material)This Question Requires You to Work with Chebychev's