If two standard normal distributions X,Y has correlation 1, are they the same random variable?

Asked Oct 23 '21 at 11:17

Active Oct 23 '21 at 11:17

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Maybe I am silly. Are these two random variables the same? Would there be any situation that they are not?

asked Oct 23 '21 at 11:17

junyaozheng98

1

Yes. That follows from condition for equality in Cauchy-Schwarz inequality. – Kavi Rama Murthy Oct 23 '21 at 11:34
Thanks for the hint! – junyaozheng98 Oct 23 '21 at 14:13

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