Thread: Hypergeometric probabilities sum to one?

Hi, Guess this should be easy, but could do with a pointer. Show directly that the set of probabilities associated with the hypergeometric distribution sum to 1. Hint: Expand the identity



So, how do you get from this to



which I take to be the formal statement of the verbal statement above, right? (i.e. the set of probabilities associated with the hypergeometric distribution sum to 1 (for a given r, w and N and where r + w = n)).

As always, much appreciated and thanks in advance for any insights.
Ta, MD

Originally Posted by Mathsdog

Hi, Guess this should be easy, but could do with a pointer. Show directly that the set of probabilities associated with the hypergeometric distribution sum to 1. Hint: Expand the identity



So, how do you get from this to



which I take to be the formal statement of the verbal statement above, right? (i.e. the set of probabilities associated with the hypergeometric distribution sum to 1 (for a given r, w and N and where r + w = n)).

As always, much appreciated and thanks in advance for any insights.
Ta, MD

As is usually the case, all the necessary clues can be found using your search engine of choice:

Hypergeometric distribution - Wikipedia, the free encyclopedia

Vandermonde's identity - Wikipedia, the free encyclopedia