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7
votes
0answers
242 views

Inequality between incomplete beta and gamma functions; or when is binomial distribution function above/below its limiting Poisson

Please note: this question was posted first (September 4) in math.stackeschange.com and then (September 16) in stats.stackeschange.com. It got no answers in neither of those sites. Let the ...
9
votes
1answer
604 views

Binomial distribution conjecture

Conjecture: Let $m$ and $n$ be fixed positive integers and let $f(k)$ be the probability that a Binomial($k(m+n)$, $p$) random variable is less than $kn$. Then for sufficiently small $p$, $f(k)$ is an ...
-1
votes
1answer
133 views

Sum of binomial probablilities

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 one question from ...
0
votes
0answers
253 views

Markov transition probabilities and negative binomial distribution.

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 is as a negative ...
6
votes
1answer
514 views

Calculating a specific joint probability involving sums of binomial distributions

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. students at our ...
0
votes
1answer
316 views

central limit theorem for binomial random variable

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($\frac{1}{n}$). Then $E[X_i]=0$ and ...
0
votes
1answer
262 views

Analytical expression for variance of nested binomials?

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) ...
8
votes
7answers
3k views

Lower bound for sum of binomial coefficients?

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 simplest case ...
2
votes
1answer
699 views

Probability of system failure in a distributed network

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 codes) at $rb$ ...
2
votes
1answer
2k views

Generalizing the wilson score confidence interval to other distributions

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 sorting criteria for ...
3
votes
3answers
2k views

Range of binomial probability, given a certain number of observations?

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 $[p_1, p_2]$ ? What is ...
1
vote
3answers
445 views

When do binomial distributions occur?

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 trials are not ...