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

question 34

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 ? 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:

Delegated Duty

A task or responsibility that is assigned by someone in authority to another person or entity to execute.

Assignor

The person who assigns contract rights.

Obligor

The party in a contractual agreement who is bound to provide a payment or performance to the other party, known as the obligee.

Third Party Beneficiary

One for whose benefit a promise is made in a contract but who is not a party to the contract.