7
votes
1answer
488 views

Has anyone seen this series?

I come across the following infinite series. $$ \sum_{n=1}^{\infty} \frac{t^n}{n!\: n^{a}}, \quad\text{for $t>0$ and $a>0$}. $$ In particular, I am interested in the case where $a=1/4$. ...
16
votes
3answers
1k views

Probabilities in a riddle involving axiom of choice

The question is about a modification of the following riddle (you can think about it before reading the answer if you like riddles, but that's not the point of my question): The Riddle: We assume ...
0
votes
1answer
183 views

Giving a general term of a recursive function, and upper bound for it

Let a constant $B \ge 1$, and let $l_1 = 0$, $b_1 = 0$ be the values of $l$ and $b$ (respectively) at time $t = 1$. Let $l_{t+1} = l_t + 1$ if $b_i < B$, and $l_{t+1} = l_t$ otherwise Let ...
2
votes
0answers
344 views

How to calculate/approximate expectation of function of a binomial random variable?

Hi, I am stuck at following problem in my research. Suppose that $M=m$ is a random variable with binomial distribution with parameters $n,p$. The constants $r$ and $\gamma$ are greater than zero. ...
4
votes
0answers
193 views

Number of times lead changes in a multi-candidate election (reference-request)

In a two candidate election where votes are distributed uniformly at random between the candidates, the probability that the lead changes when tallying the $i$-th vote is the same as the probability ...
18
votes
3answers
1k views

Zeroes of the random Fibonacci sequence

Let X_n be the "random Fibonacci sequence," defined as follows: $X_0 = 0, X_1 = 1$; $X_n = \pm X_{n-1} \pm X_{n-2}$, where the signs are chosen by independent 50/50 coinflips. It is known that ...
0
votes
1answer
185 views

Distribution wanted

I have a centered random variables $Y_1,Y_2$ which first 10 moments are given respectively by $$ 0, 1, 0, 6, 0, 90, 0, 2520, 0, 113400 $$ $$0, 1, 0, 32/3, 0, 36847/100, 0, 436879364/15435, 0, ...
25
votes
2answers
1k views

“Are you more intelligent than the average of those who are more intelligent than the average?”

I'm sure that many MO users would answer "Oh, yes, I'm more intelligent than the average intelligence of the population that has an intelligence greater than the (absolute) average". And someone, less ...
20
votes
5answers
794 views

Iterated Circumcircle

Take three noncollinear points (a,b,c), compute the center of their circumcircle x, and replace a random one of a,b,c with x. Repeat. It seems this process may converge to a point, assuming no ...
0
votes
0answers
385 views

Who finishes first? probability problem

Consider the following scenario: We have a number of sequential building blocks (e.g. 12 building blocks, ordered from 1 to 12), distributed randomly (but not necessarily equally) on a number of ...
2
votes
4answers
12k views

limsup and liminf for a sequence of sets

how does limsup and liminf for a sequence of sets, apply to probability theory. any real world examples would be much appreciated