One of my friends is building a game where the player will get questions from 6 different categories. Each category has a total of 50 questions. A single game consists of answering …

Consider a story ranking website in which the ranking is crowd sourced from the number of up votes and down votes received by a story. The score is computed as the lower bound Wil …

A realization of a Markov process generates a sequence of interval lengths between transition from one state to another. A natural way of modeling the distribution of the lengths i …

The following might look like a simple problem - but the question has been unanswered for more than a week on math.stackexchange.com, and I have asked quite a few of the Ph.d. stud …

I'm confused about applying central limit theorem to Bernoulli random variables. Let $X_i=\frac{n}{\sqrt{n-1}}(Z_i - \frac{1}{n})$ where $Z_i$ is iid Bernoulli($\frac{1}{n}$). The …

Hi! I'm new here. It would be awesome if someone knows a good answer. Is there a good lower bound for the tail of sums of binomial coefficients? I'm particularly interested in the …

Hi all, I want to compute the variance of a variable that is defined at each step as a recursion of binomials in the following way: A=1 B=Bin(1,A)*Bin(1,p) C=Bin(1,B)*Bin(1,p) …

A binomial distribution is the distribution of the number of successes of n independent, identical Bernoulli trials. What happens when the trials are dependent and the Bernoulli t …

This article describes the 'Wilson score confidence interval', and describes how to use it to derive the lower bound on the nth percentile confidence interval for determining sorti …

I am trying to build a mathematical model of the availability of a file in a distributed file-system. The system works like this: a node $x$ stores a file $f$ (encoed using erasure …

Let's say I am given $n$ flips of a coin, $k$ of which are heads. These are iid flips. Can I say, with probability $p > 1/2$, that the true probability of heads is in range $[p_1, …