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

question 18

Essay

(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 δ 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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Definitions:

Social Facts

Aspects of social life that shape an individual's actions, such as norms, values, and beliefs, according to sociologist Émile Durkheim.

Political Beliefs

The convictions or opinions individuals hold about political issues, policies, and personalities.

Lumpenproletariat

A term used in Marxist theory to describe the underclass, excluded from the class structure of capitalist society, without access to the means of production.

Critical Distance

Critical distance involves maintaining an analytical perspective that allows for objective evaluation and critique of a subject, avoiding personal bias or emotional involvement.