Let X and Y be two independent and identically distributed random variables with expected value 1...

Let X and Y be two independent and identically distributed random variables with expected value 1 and variance 2.56.

(i) Find a non-trivial upper bound for P(|X + Y − 2| ≥ 1). 5 MARKS

(ii) Now suppose that X and Y are independent and identically distributed N(1, 2.56) random variables. What is P(|X + Y − 2| ≥ 1) exactly? Briefly, state your reasoning. 2 MARKS

(iii) Why is the upper bound you obtained in Part (i) so different from the exact probability you obtained in Part (ii)?

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Expert Solution

orchestra answered 1 year ago

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