same cdf equals same expectation?

Question

So, if $X$ and $Y$ are both continuous random variables with the same cdf, does that mean that their expectations are the same? And the same thing in case $X$ and $Y$ are both discrete.
Thanks in advance!

markowitz · Answer

Cumulative Distribution Function (CDF) characterizes exhaustively any random variables. So if two rv's share the same CDF these are identical. Then yes, they are the same expected value if it exist. We can say more, these two rv's share all moments.
More interesting to study the situation in which two rv's share some moments. In this case is not sure that the them are identical (same CDF).

same cdf equals same expectation?

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