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If I have independent and identically distributed random variables $X_1, \dots, X_n$, then are $f(X_1), \dots, f(X_n)$ themselves independent and identically distributed?

I think the answer is yes, and assuming $f$ is nice enough (e.g. measurable), and the result is almost immediate. But I'm just hoping for a sanity check.

Thank you.

caitlin
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    Yes, that's correct. See e.g. https://stats.stackexchange.com/questions/94872/functions-of-independent-random-variables for the independence aspect. The fact that they're identically distributed is even easier to show. – S. Catterall Nov 06 '23 at 18:15

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