Recent content by ClifDavis

Yeah, I will admit to being curious about what viraltux thinks "cardinality of the intersection" does relate to.

I agree. In fact judging by his initial attempt at a solution it really seems to be what he had in mind from the beginning. In fact, my question to him should be read, "given that each ball is picked by each person with a probability p, if you had taken the probability that the first k balls...

David, going back and rereading what I wrote I can see where I could give the impression that simply correcting the last part of your expression to ({(K\choose k}p^k(1-p)^{K-k})^{M-1} would fix all you problems. It wouldn't. That expression would give the probability that all M people would...

Now that we know what the actual problem is we can see where his {K\choose k}p^k(1-p)^{K-k} came from. You have the probability of getting k picks followed by K-k non-picks, which gives you one instance of picking k balls and since any selection of k balls is equally probable you multiply by...

In order to answer the question it is not necessary to know the number of picked balls a priori. It is however necessary to know the probability distribution of the number of balls picked. If there are M=2 people and K=5 distinct balls and there is a very high probability of 4 or 5 balls...

Okay let me restate the problem to see if I understand it correctly. There are M people and K distinct balls. Each of those M people will pick a number k at random between one and K inclusive and then pick k balls at random. An reliable observer will record which balls they picked. Then...

David, I understand that this is not the actual problem you want to solve. What is the problem you want to solve?

Yep, though he seemed to be familiar that part of it okay up front and was fine with the idea as applied to A(k). I appreciate the mini-tutorial on solving homogeneous recurrence relationships by the way. I've probably seen that at one point or another but have long since forgotten. Just...

Okay, try #2 and I'll try to be a bit shorter this time. SeventhSigma, just in case it isn't clear, haruspex is looking at the family of functions that have the same recurrence formula as Count except that they are missing the final two terms 25*2^(n-7)-1. Based on some of that theory I...

Dammit, I had a free hour and just tried to post a longish comparison of our two suggestions and then when I went to submit it claimed I wasn't logged in. though it let me answer SeventhSigma just before. And the post seems to be irretrievable. :-( Very aggravating And now I don't have a...

Yes, but I don't know what it is. :-| There is an advanced study of recurrence relationships and solving difference equations in general. Some of which is then used in solving certain types of differential equations. I think that haruspex may be more familiar with some of the general...

The last time around, in order to develop the M matrix we've been using, I got rid of the Countnew function and expressed Count solely in terms of older values. But for what we are about to do, I want to drop back to a slightly more transparent version. We have: C(1)=0 C(2)=1 C(3)=3 C(n)=...

Yay! It's Thursday. And of course other things have come up, but we'll see how it goes. My original approach to this was a bit different than haruspex's clever approach to the problem where he works with C(n) and D(n). Instead I worked at building a recurrence formula for Count(n) directly...

Thanks, I never know when my explanations are adequate and when they are as clear as mud.

I'm going to assume now that you are using the transpose of M and multiplying by a column vector. To write a column vector as a row vector I'm going to use the ^T to indicate transpose as in vectors V and V^T We want to use the functions defined by: C(1)=0 C(2)=1 C(3)=3 C(n)=...