I was trying to prove this statement in a formal way although intuitively it sounds true. is there any better and fast way to conclude this other than trying to see if the cumulative distribution function of $X, Z$ is equal to that of $X, Y$?
2026-03-30 00:22:59.1774830179
If X and Y are independent random variables, then, are X and $Z= Y+1$ independent random variables?
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