# Questions tagged [bernoulli-trial]

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1answer
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### Distribution of a two-part sampling process

I have a known distribution $f(x)$ (in fact, I can safely assume that $f(x)$ is the Maxwell-Boltzmann distribution, i.e. $f(x)\propto x^2 \exp(-x^2)$). I take $N$ samples from the distribution, but am ...
1answer
123 views

### How to prove this “obvious” result from Bernoulli trials / partial Pascal series?

The main problem setup - very brief I need to prove that the following two equations have a solution with $CAP=v$. 0= ( CAP - C ) \sum_{j=1}^J j N \cdot q^{j-1} (1-q)^{N -1-j} \binom{N}{j} ...
0answers
180 views

### $X-Y$, where $X$ and $Y$ are sums of Bernoulli random variables

Let $X = x_1 + x_2 + \ldots + x_n$ and $Y = y_1 + y_2 + \ldots + y_n$, where each $x_i$ is an independent Bernoulli random variable with success probability $p_i$ and each $y_i$ is a Bernoulli random ...
0answers
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### How fast does a sum of Bernoulli distributions (of different parameters) decrease after its mean?

Let $X=\sum_{i=1}^nX_i$, where each $X_i$ is a random variable following a Bernoulli distribution of parameter $p_i$. All $X_i$ are independent, and for all $i$, $p_i<p$ for some small $p$. I'm ...
2answers
558 views

### Can the sum of identically distributed dependent Bernoulli trials be binomially distributed?

If you have $n$ identically distributed Bernoulli trials whose sum is binomially distributed random variable, does it then follow that the $n$ Bernoulli trials are independent?
1answer
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1answer
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1answer
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### Generating Bernoulli Correlated Random Variables with Space Decaying Correlations

Hi, I have a set of N objects randomly distributed in a 2D physical space. Each object (i) generates a bernoulli random number (0 or 1) based on a marginal probability Pr(xi = 1) = p. These objects a ...
1answer
145 views

### References for Poisson and Lexis trials

I have been trying to find more information on Poisson and Lexis trials (generalizations of Bernoulli trials), but I have failed to find anything outside of MathWorld (I went through a number of ...
3answers
640 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 ...