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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How to derive instant-dependent regret for KL-UCB bandit?
I was reading KL-UCB algorithm for bandit with Bernoulli reward from Bandit Algorithms book by Lattimore (Section 10.2), and the regret provided by the algorithm is instant-dependent and it depends on ...
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Number of successes for correlated Bernoulli variables
The number of successes for a given set of independent Bernoulli random variables is described by the binomial distribution. However, I was wondering what could be said if the Bernoulli variables were ...
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With $X$ and $Y$ being two independent $\text{Bernoulli(1/3)}$ rvs, show whether $U = |Y-X|,~V = X+Y$ are independent or not
Let $X$ and $Y$ be two independent $\text{Bernoulli(1/3)}$ random variables. Define random variables $U$ and $V$ as $$U = |Y-X|, \hspace{5mm} V = X+Y$$ Are $U$ and $V$ independent?
I am new to the ...
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Calculating contrasts of marginal effects with marginaleffects for brms model
I have fitted a logistic model with brms and want to calculate the average marginal effects (AMEs).
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Point estimate of exponential distribution [closed]
Let $X_1, ..., X_n \sim Exp(\lambda)$ What's the probability $p$ that $X > 1$ for $X \sim Exp(\lambda)$.
$p$ should be $e^{-\lambda*1}$
I want to use only the following method for point estimate $p$...
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For what kind of distributions could the joint distribution be determined uniquely by marginal distribution and correlation?
Assume $X$ and $Y$ are from the same distribution $P$ and $\rho = \frac{Cov(X,Y)}{\sqrt{Var(X)Var(Y)}}$ is fixed. For what kind of $P$ can we determine uniquely the joint distribution of $X,Y$?
I know ...
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Central Limit Theorem to determine sample size
Given a sample $X_1, ..., X_n \sim^{iid} $ Bern(p). I want to test $H_0: p = 0.49$ vs. $H_1: p = 0.51$.
How can I determine the sample size for which the probability of type I error (and type II error)...
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Multi-armed bandit with 2 coins: What strategy maximises reward?
What strategy maximises the total reward, on average, after $n$ trials, in this multi-armed bandit:
two coins A and B, with probability of success $p_A$ and $p_B$
reward is $1$ on success, $0$ on ...
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Concentration bound for weighted sum of Bernoullis
$\{X_i\}_{i=1,\ldots,n}$ are i.i.d. Bernoulli random variables with parameter $p$. Define
$$Y = \sum_{i=1}^n a_iX_i$$
where $a_i>0$ are known(non-random) constants. I want an upper bound on the ...
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Expectation & Covariance matrix of indicator vector
Suppose we have the $p$-dimensional random vector $\boldsymbol{X} \sim \mathcal{N}(\boldsymbol{\mu}, \Sigma)$. Take the set $A$ to be (without loss of generality) the negative real line, thus $A = (- \...
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Generate Correlated Bernoulli Samples in Python
Suppose I have $M$ Bernoulli distributions with parameters $p_i$, pairwise correlation $\rho_{ij}$ for $i\neq j$. I would like to generate $N$ samples from the joint distribution. The case of $M=2$ ...
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Are there exact conditional tests for testing system of inequalities of Bernoulli means?
I have two independent Bernoulli samples: $\{X_i\}_{i=1}^{n_1}$, $\{Y_i\}_{i=1}^{n_2}$, $X_i \overset{iid}{\sim} Bern(p_1), Y_i \overset{iid}{\sim} Bern(p_2)$. I need to test:
$$H_0: p_1 \ge p_2 \ge 1/...
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Finding covariance structure for Bernoulli GLMM (Random Intercept)
How does one find the covariance structure theoretically for a Bernoulli GLM?
For Normal LMMs ($y_{ik} = x_i^T\beta + \epsilon_i + u_k$) it's quite straight forward. For observations within the same ...
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Simulate bivariate bernoulli responses with predefined beta coefficients
I have a specific data matrix with features (mainly categorical). I want to simulate a multivariate bernoulli response, for example bivariate, but with a predefined vector of beta coefficients (most ...
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PMF of the Independent Multivariate Bernoulli Distribution
I was reading this paper on the Multivariate Bernoulli Distribution, which provides the general form of the PMF in equation 3.1. The paper refers to this as the probability distribution function, but ...
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