# Tagged Questions

**0**

votes

**0**answers

4 views

### Probability of differently loaded dice summing to a value

I have a real world problem that boils down to the following:
I'm playing dice. I have $n \approx o(10)$ differently biased die. The probability of the $i^{th}$ die showing $x_i$ is given by ...

**4**

votes

**2**answers

152 views

### Joint probability distribution as functions

Suppose $X$ and $Y$ are correlated random variables in a finite set ${\mathcal A}$, and let $f, g$ be functions that map elements from ${\mathcal A}$ to ${\mathcal B}$ for some finite set ${\mathcal ...

**7**

votes

**2**answers

256 views

### How to efficiently sample uniformly from the set of p-partitions of an n-set?

Let $n,p \in \mathbb{N}_+$ with $p \leq n.$ Let $\mathcal{P}$ denote the set of partitions of $\{1, \ldots, n\}$ into $p$ nonempty sets. How can I efficiently sample uniformly from $\mathcal{P}$?

**1**

vote

**0**answers

323 views

### Prove that the sum of a certain infinite series is 1

Prove the (numerically-evident) proposition that
\begin{equation}
\Sigma_{i=0}^\infty f(i) = 1,
\end{equation}
where
\begin{equation}
f(i)= 2^{-4 i-6} q(i) \frac{\Gamma(3 i+\frac{5}{2}) \Gamma(5 ...

**7**

votes

**2**answers

349 views

### Concentration bounds for sums of random variables of permutations

I'm trying to find theorems regarding random variables derived from sampling permutations, specifically concentration bounds.
As an example, let $X_i$ be the $\{0,1\}$-random variable that represents ...

**2**

votes

**2**answers

308 views

### Sampling without replacement until hitting a subset

I randomly sample uniformly from $ \{1,..,N \}$ without replacement until drawing a number $ \leq k$. Denote the expected number of draws by $R(N,k)$. I want a good approximation for $\sum_{k=1}^N ...

**1**

vote

**1**answer

276 views

### Azuma's Inequality when the conditions hold with high probability?

In Azuma's Inequality, is the statement true when $|X_k - X_{k-1}| < c_k$ almost surely rather than with probability 1? If not, is there another result which gives strong concentration when the ...

**1**

vote

**1**answer

125 views

### The degrees in a random subgraph

Fix some positive integers $N$ and $d_k$, $k=1,2,\dots$ with $N=\sum_{k=1}^\infty d_k$.
Suppose you have a graph $G$ taken randomly uniformly among the set of all (unoriented) graphs with $N$ ...

**8**

votes

**3**answers

477 views

### A Variance-Tail Description for Continuous Probability Distributions

Start with a continuous probability distribution given by a density function f(x). Let X be a real random variable whose distribution is given by the probability distribution.
I would like to ask ...

**5**

votes

**1**answer

197 views

### Is the maximum tree-path length distributed lognormally (in the limit) ?

Consider a full binary tree with $k>10$ levels. Let the lengths of individual edges in this tree be i.i.d. random variables with finite moments. Then total lengths of the $2^{k-1}$ source-to-sink ...

**4**

votes

**2**answers

249 views

### Distribution of the biggest gap

Randomly select $n$ numbers from the universe $\{1,2\dots,m\}$ 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 can ...

**2**

votes

**2**answers

458 views

### A large deviation / binomial coefficients bound

Maple seems to suggest that for any real $a\ge 1$ and positive integer $K$ and $n$ with $K\le n/(a+1)$ one has
$$ a^n + na^{n-1} + \binom{n}{2}a^{n-2} +...+ \binom{n}{K}a^{n-K} \le a^{n-K} ...