Prove that if we have n independent events any subset of them is independent?

I am in a class that is defining independence a little differently, it uses random variables instead of events in the definition (you can extend it to events using indicator functions). Either way I don't think that specific definition matters here.





What I need to show that is if we have n independent random events then any k%26lt;=n, k%26gt;1, of them are still independent.





e.g. If you have 4 independent events then show any pair is also independent. I guess I'm on a stumbling block on what exactly there is to prove. Thanks for your help.

Prove that if we have n independent events any subset of them is independent?
Regardless of the definition you can easily prove the hypothesis. Start out by assuming(for contradiction) that a subset of k events are not independent. It would follow that the original n events are not independent. This contradicts the given information. Consequently the k events must be independent.