Let X and Y be independent and identically distributed random variables. For each of the following questions,

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 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?

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...

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