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Seating assignment inspired question

Motivation. Recently I stayed at a hotel which had the curious custom to ask their $n$ parties (group of guests, most parties a married couple) which of the $n$ tables they wanted to take. Of course ...
Dominic van der Zypen's user avatar
16 votes
0 answers
309 views

Randomized Pascal's triangle: What is the average of all the numbers?

This question was posted on MSE. It received some interesting responses, but no definite answer. Let's build a variation of Pascal's triangle. We write $1$'s going down the sides, as usual. Then for ...
Dan's user avatar
  • 3,547
0 votes
0 answers
134 views

Asymptotics of a ratio on the unit sphere

Let $(a_n)_{n \geq 1}$ be a nonnegative, strictly decreasing sequence with $a_n \to 0$ as $n \to \infty$. Consider the ratio (for $k \geq n$) $$ R_{n, k} = \mathbb{E}_{u \sim \text{Unif}(\mathbb{S}^{k-...
Drew Brady's user avatar
1 vote
0 answers
36 views

Uniform distribution as argument for copula likelihood

I am reading a well-known paper about copulas by Chen and Fan (2006). Specifically, Proposition 4.2 (see attached), in which all the arguments are uniform $U_{t-1}, U_t$. However, when the copula is ...
Grigori's user avatar
  • 33
0 votes
1 answer
197 views

Bound the expectation of an average

Let $(a_n)_{n \geq 1}$ be random variables taking values on a finite subset $B$. Assume that $\nu_l(b) \le P[a_n = b\mid a_1,\ldots,a_{n-1}] \le \nu_u(b)$ almost surely for every $n \ge 1$ and $b \in ...
Star's user avatar
  • 108
3 votes
1 answer
473 views

Expected value of the maximum of the periodogram

Let us suppose that $X_1,\ldots,X_n$ with $n\ge1$ are iid random variables such that $\operatorname EX_1=0$ and $\operatorname E|X_1|^s<\infty$ with some $s>2$ and define the DFT of $X_1,\ldots,...
Cm7F7Bb's user avatar
  • 423