Questions tagged [combinatorics]
Counting or enumerating elements in a set or other finite discrete structure.
554
questions
4
votes
2
answers
67
views
Making 3 comparisons with a ternary variable
I have a study in which I want to study the effect of a ternary variable $x$ in interaction with a binary variable $y$. The ternary variable is categorical, and for some reasons, I want to do the $3$ ...
1
vote
1
answer
42
views
10 identical socks, 7 drawers: What is the probability that at least one drawer contains 3 or more socks?
My nephew asked me the question thinking I would answer him very quickly, but I got stuck until today.....
There are 7 drawers and 10 socks, all the same. The socks are randomly distributed in the ...
- 243
0
votes
0
answers
26
views
Combinatorics question
Let me preface this by saying that this might be a trivial question for some of you.
I want to find a formula that will help me automatically calculate the number of occurrences of certain kind of ...
- 1
0
votes
1
answer
66
views
How to solve this "easy" probability problem
I'm struggling on how can I solve the following problem. I tried with a lot of calculus without success, but i think that the way to solve is:
$$P(\text{at least one failure})=1−P(\text{no failures in ...
- 280
0
votes
0
answers
12
views
What is the Pseudo dimension for Lipschitz function class?
I am trying to get a bound on covering numbers with $L_2(P_n)$ norm using pseudo-dimension or fat-shattering numbers for Lipschitz classes.
1
vote
1
answer
44
views
Supposed to be a simple question about entropy
Let say there is an urn which contains balls of different color. It is a well known formula to calculate entropy of balls in the urn:
$H = - \sum P_i\cdot\log(P_i)$
where $P_i = \frac{M_i}{N}$, where $...
- 121
5
votes
1
answer
152
views
Statistical tests for data on occurrence of reptiles found under different types of artifical cover objects
I am studying small-bodied ground snakes and skinks (lizards). I use artifical cover objects to determine their presence.
Artificial cover objects (hereafter CO) consisting of 7 different types of ...
- 53
4
votes
1
answer
84
views
Conditional expectation of Poisson, conditional on Poisson sums
Consider independent Poisson random variables $X_1\sim \text{Poisson}(\alpha_1)$, $X_2\sim \text{Poisson}(\alpha_2)$, $Y\sim \text{Poisson}(\lambda)$, and suppose $Z_1=X_1+Y$ and $Z_2=X_2+Y$. I want ...
- 850
1
vote
0
answers
35
views
Enumerating feasible solutions to the subset sum problem using Gibbs sampling
Given a set of $m$ strictly positive real numbers $W = \{ w_{1}, \dots, w_{m} \}$, I want to find subsets of $W$ whose sum is less than or equal to a maximum value $N$ using Gibbs sampling. To do this,...
- 101
2
votes
1
answer
41
views
Combinatorics: create a 3-digit number out of 2 digits?
We have a set of two numbers {1,2} an we wish to create a 3-digit number out of the two numbers without order mattering. Here is my approach since there are 2 values for each spot then it's 2^3 since ...
- 23
0
votes
0
answers
64
views
Probability of 5 card texas holdem poker royal flush
How would I calculate the probability of getting a royal flush with 2 player Texas holdem poker.
A single randomly shuffled 52 card deck, 2 players (p1 & p2) are sequentially dealt 4 cards i.e. p1 ...
- 11
1
vote
0
answers
102
views
Probability problem - Jackpots
The rules of the final round of King's Lottery in Byteland are simple:
The player starts to draw balls from an opaque bag containing $a$ red balls, $b$ green balls and $c$ blue balls initially.
After ...
3
votes
2
answers
83
views
What is the probability of being dealt two pairs when all $\binom{52}{5}$ poker hands are equally likely?
Question from Sheldon Ross's First Course in Probability, Chapter 2:
If it is assumed that all $\binom{52}{5}$ poker hands are equally likely, what is the probability of being dealt two pairs? (This ...
- 31
1
vote
0
answers
58
views
Generate unbalanced sample [closed]
Suppose we have $N$ individuals consisting of two different groups, A and B. Each group contains $N/2$ people. The label of each individual $Z$ follows a binary distribution with probability $P(Z=A)=P(...
- 121
0
votes
0
answers
14
views
Conditionally Quasi-random Choices and Qualitative Dependent Variable Models
I have a scenario about limited dependent variable models and some of their implications. Suppose that I estimate some limited dependent model, it does not really matter which one, that captures the ...
- 303