Given "N" number of events, calculate the number of condition to check whether all the events are statistically independent.

Question

please help me out here, i dont even know where to start with this question :(. Any guidelines anything at all that may give me an idea to answering the question will be greatly appreciated.

Please also suggest any book that covers this kind of problems.

Thanks.

Answer 1

You have to proof if all the combinations of the events are independent.

pairwise comparision:

number of conditions: $n \choose 2$. That is the number of all combinations of two events from n events.

Then you have to prove $P(A_i \cap A_j \cap A_k)=P(A_i)\cdot P(A_j)\cdot P(A_k) \ \quad \forall i\neq j \neq k; i,j,k=1,..,,n$

number of condition.:$n \choose 3$

If you go on like this, you have $\sum_{k=2}^n {n \choose k}$ conditions for n events. This can be simplified by using the Binomial Theorem.