The binomial-distribution tag has no wiki summary.

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### Expected centered entropy of the binomial distribution

In short, the function I am interested in is the following:
$$I_n(p) = \sum_{k=0}^n \binom{n}{k} p^k (1-p)^{n-k} \left[h(p) - h\left(\tfrac{k}{n}\right)\right],$$
where $h(x) \triangleq -x \log x - ...

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**0**answers

331 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 ...

**10**

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**1**answer

620 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 ...

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**1**answer

140 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**

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**0**answers

373 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

**1**answer

536 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

**1**answer

402 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

**1**answer

271 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)
...

**9**

votes

**7**answers

4k 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

**1**answer

776 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

**1**answer

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

**3**answers

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 ...

**2**

votes

**3**answers

519 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 ...