# Independent random variables defined over same probability space with same distribution [closed]

Is it possible that two real random variables $X_1,X_2$ are defined in the same probability space $(Ω,F,P)$ and have the same distribution and be independent ?

## closed as unclear what you're asking by Did, erfink, Shailesh, Daniel W. Farlow, LeucippusJul 23 '17 at 1:30

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• please provide reasoning for downvoting . – liaguridio Jul 22 '17 at 16:31
• Why are you duplicating existing questions/answers? – Did Jul 22 '17 at 16:32

I throw a penny and a dime. $X_1$ is the event that the penny is $H$, $X_2$ is the event that the dime is $H$.