# Questions tagged [bernoulli-distribution]

The Bernoulli distribution is a discrete distribution parametrized by a single "success" probability. It is a special case of the binomial distribution.

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### Test for a Bernoulli model with a single trial

I have a model that predicts Bernoulli probability parameters $p_i$ at $i\in[1..100]$ sites. To test this model, i can only take one trial at each one of the sites, resulting in $\approx10$ successes....
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### How can I derive the EM algorithm for a mixture of two Bernoulli distributions?

How can I derive the E-step and M-step in the EM algorithm for a mixture of two Bernoulli distributions? Note that I am aware that there are several notes online that explain how to do this for the ...
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### Why does redrawing a sample of a binary variable split into two groups generate different distributions according to prop.test()?

I was working on some power calculations and stumbled upon results I don't understand. Say we have a sample of a binary variable a, and the sample probability of success is p. We randomly split the ...
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### How to find the median of Bernoulli trials and $\bar{X} = (X_1 + X_2 + X_3)/3$?

Assume $X_{1}, X_{2}$ and $X_{3}$ are independent Bernoulli trials with $p=0.5 .$ Let $\bar{X}=\left(X_{1}+X_{2}+X_{3}\right) / 3$ and $M=\operatorname{median}\left(X_{1}, X_{2}, X_{3}\right)$. (a) ...
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### Absolute of expected value of multivariate correlated Bernoulli

I am running some experiment where I draw samples from a multivariate Bernoulli distribution (in this case taking values -1 or +1) with a single correlation coefficient (i.e., same correlation for all ...
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### Efficiency of two estimators for a sample from a Bernoulli population

Given a Bernoulli population, I have two estimators for a random sample of size $n$: $T_1=\frac{\sum\limits_{i=1}^n X_i + 2X_n}{n+2}$ $T_2=\frac{\sum\limits_{i=1}^{n-2} X_i + 2X_n}{n+2}$ I want to ...
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### What would be the proper distribution to model the number of particles in a state in canonical ensemble

Suppose my system has $N$ particles, and I want to find a distribution for $n_i$, the number of particles in the $\epsilon_i$ energy state. What I do know is the boltzmann probability, which tells me ...
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### Bayesian inference - Calculating the prior distribution of the parameter in the Bernouli distribution from a series of bernouli proccesses

What I have are n different time series of bernouli processes of varying lengths, taking the values of 0 or 1. What I would like to do is to use Bayesian inference to calculate, for one of these ...
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### Confindence Intervals for Ordinal Variable

I count how many days within a month people have executed a certain activity. The maximum is 30 (i.e., the person executed the activity each day), the minimum is 0 (i.e., the person never executed the ...
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### Hypothesis Testing on Derived Distributions

Suppose we have access to samples from two probability distributions $P$ and $Q$ which may be arbitrary and high dimensional but are over the same domain $\mathbb{X}$ (for example $P$ and $Q$ may be ...