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

7.

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)

(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.

(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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