Statistical independence proof help

Hello all,please help me with this problem, i am busy studying for a test and am stuck on this. [Question]Given "N" number of events, calculate the number of condition to check whether all the events are statistically independent. [Solution]I have been given the procedure but have no idea how to go about following the instructions: please see the attached picture.

What I am understanding about the problem is that the attached picture gives the number of conditions one way and you need to write that in a different form using the Binomial Theorem. Therefore you need to find out what the Binomial Theorem is. Not only that, you should remember it as it may come up on other tests in the future. To save you a bit of time, this is the formula for it


( from http://en.wikipedia.org/wiki/Binomial_theorem )

As a hint, comparing the attachment to the above we see that we are missing the terms for 0 and 1 in the attachment. So using the formula above, we would have to subtract out the value of those terms. Also note that 1ⁿ =1 for all n.

Ishuda said:

What I am understanding about the problem is that the attached picture gives the number of conditions one way and you need to write that in a different form using the Binomial Theorem. Therefore you need to find out what the Binomial Theorem is. Not only that, you should remember it as it may come up on other tests in the future. To save you a bit of time, this is the formula for it

( from http://en.wikipedia.org/wiki/Binomial_theorem )

As a hint, comparing the attachment to the above we see that we are missing the terms for 0 and 1 in the attachment. So using the formula above, we would have to subtract out the value of those terms. Also note that 1ⁿ =1 for all n.

Click to expand...

Thanks a lot.