0
votes
0answers
21 views

Pairwise independent subsets of fixed size

For a given set $\Omega$ of even size $n$, does there exists, in general, a collection of subsets $F \subset 2^\Omega$ such that $\forall A \in F. |A| = \frac{n}{2}$, $\forall \omega \in \Omega. ...
1
vote
1answer
37 views

Choosing a sample from a sample probability

I am a bit confused about this problem. I understand that you need to pick a sample first, K, and then find the probability of that sample being red, L. The total different combinations of picking a ...
1
vote
1answer
224 views

probability of a certain event in a repeated sampling with replacement (without ordering)

I have a problem that is bugging me for a couple of weeks now. I have asked some friends etc but the answers were not satisfying at all. So here we go. Suppose we have a set ...
1
vote
2answers
178 views

Sampling a combination randomly

I want to sample a combination of $N$ elements (without replacement) from a list of $M$ elements where $M\gg N$. There are algorithms to do this when each element is picked with uniform probability. I ...
11
votes
2answers
428 views

What is the distribution of gaps?

Randomly select $n$ numbers from the universe $\{1,2\dots,m\}$ with or without replacement, and sort the numbers in ascending order. We can get a list of number $\{a_1,a_2,\dots,a_n\}$, and then we ...