Question: Let X and Y be independent and identically distributed random variables. For each of the following questions, either show that it is true or exhibit

Let X and Y be independent and identically distributed random variables. For each of the following questions, either show that it is true or exhibit a counter-example.
(a) Does X + Y have the same distribution as 2X?
(b) Does X + Y have the same expectation as 2X?
(c) Does X + Y have the same variance as 2X?

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