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Results tagged with pr.probability
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user 15837
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
4
votes
expected number of balls in k emptiest bins
This is only a very partial answer, and I would have considered putting it as a comment if I were a more reputable contributor, but I hope it's at least somewhat helpful.
Consider the simplest possib …
- 5,432
5
votes
Mean minimum distance for N random points on a unit square (plane)
The OP's intuition goes awry in the very first case, $N=2$, where it predicts an expected distance of 1. As I'll show below, the expected distance between two points in the unit square is less than 1 …
- 5,432
14
votes
Boys and Girls Revisited
This is just a variant presentation of fedja's truly wonderful solution. It took me a while to catch on to the idea there, so I'm offering this in case it helps clarify it for anyone else. All credi …
- 5,432
10
votes
Accepted
Anyone has Kushner's book "Introduction to stochastic control" 1971? I need a theorem from it
The Carleton College library has a copy of the Kushner book. Here's the theorem:
Theorem 8
Let* $P\gt0, C\ge0$ and
$$EA_n'PA_n-P=-C.\ \ \ (8.24)$$
Then $EX_n'CX_n\rig …
- 5,432
8
votes
Path length of ball on tilted, perforated plane
This is just a small streamlining of Douglas Zare's proof that the expected length $L(\epsilon)$ is infinite when $\epsilon < 1/2$.
The expected length will only decrease if you enlarge the holes to …
- 5,432
3
votes
Collisions between rooks taking random flights on an N by M chessboard
It occurred to me it might be of interest to see what happens if you start with a board completely clogged with rooks*, so I decided to pluck the lowest-hanging nontrivial fruit and examine the $2\tim …
- 5,432
1
vote
A Pascal's-triangle -like random process
The basic structure of the numbers you get is invariant under affine transformations, from $(a,b,c,d)$ to $(ra+u,rb+u,rc+u,rd+u)$, so you may as well assume you're working with integers that sum to 0 …
- 5,432
3
votes
How many boxes so that there is $k$ of same of color from $n$ different colors?
Googling on "birthday problem 1995" turns up references to a paper by L. Holst, the abstract to which reads
The general birthday problem with unlike birth probabilities and the
waiting time N un …
- 5,432