Tagged Questions

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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Combined confidence of hit/miss results from 20 different test subjects

I'm a computer science student and statistics isn't my strong suite. I would appreciate some help. I did a task performance experiment for my Master's thesis to validate my "special secret ...
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A variation of binomial model with gain associated with each success

I am trying to develop my first machine learning model. Each example k in data has [#trials(k), #successes(k), gain(k)]. So total gain for example k is ...
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random variable and bernoulli distrbution

I was asked the following question: X is a random variable which follows a Bernoulli distribution with parameter p and take $Y=a+bX$. Compute $\mathbb{E}(Y^3)$. Can anyone please help me.
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Independence in a Joint Bernoulli distribution

Given that [X = 1] and [Y = 1] are independent in a joint Bernoulli distribution, how do we show that X and Y are independent?
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Variance of a product of Bernoulli with another distribution

This is probably a stupid question, so my apologies if this is too simple. I have a distribution X, now I play the following game: I toss a coin, if it falls on a head, I get nothing, if it falls on ...
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Convergence of standardized means of a Bernoulli variable / CLT

The Question Consider a binary random variable X that satisfies: $Pr(X = 0) = \theta \ \ \$ and $Pr(X = 1) = 1âˆ’\theta$ for $\theta \in (0, 1)$ an unknown parameter. Suppose an i.i.d. sample of size ...
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Hypothesis Test on Contest, a problems?

We have a contest 1 weeks ago. One question is a bit strange for us as follows: $X\sim B(4,p).$ for test $H_0:p=0.2$ versus $H_1:p>0.2$. if $X=4$, $H_0$ assumption is rejected. calculate ...
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Dependent Bernoulli trials confidence interval

I would like to know if there is a way to build a confidence interval, for a random variable which has a Bernoulli distribution, based on its history. I mean if the order of its states is 11100 (i.e. ...
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Number of trials necessary to demonstrate Bernoulli process doesn't have mean p

I have a Bernoulli process that purportedly has mean $x$ but I hypothesize that the process actually has mean $q$. How many trials are necessary to demonstrate (to some confidence $p$) that the actual ...
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How to compute the PDF of a sum of bernoulli and normal variables analytically?

Can convolution be applied to get a closed form expression for $Z = X + N$ where $X$ is a Bernoulli random variable and $N$ is a zero mean normal random variable independent of $X$?
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Logistic Regression: Bernoulli vs. Binomial Response Variables

I want to perform logistic regression with the following binomial response and with $X_1$ and $X_2$ as my predictors. I can present the same data as Bernoulli responses in the following format. ...
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Zero-inflated Poisson and Gibbs sampling, proofs and sampling

I am trying to figure out zip-inflated Poisson (ZIP) model. In this model, random data $X_1, .., X_n$ are of the form $X_i=R_iY_i$, where the $Y_i$'s have Poisson distribution ($\lambda$) and the ...
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Is a random variable Bernoulli? Is a proof available?

Suppose a die is tossed twelve times and each outcome is represented by a random variable $X_{i}$. Further define $Y_{i}$ for $i=2,...,12$ to take the value $1$ if $X_i=X_{i-1}$ and $0$ otherwise. ...
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Sampling Twice and Posteriors

I have a random variable with some unknown distribution with support over $[0, 1]$. Every turn, I sample a $p_t$ from this distribution. However, I am unable to observe $p_t$ directly. Instead I ...
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Which distribution should I better use to predict the response in {0,20} applying GBM? [duplicate]

I want to predict the response that is in {0,20}. I am using GBM to make the prediction. ...
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Maximum Entropy with no index

This is a simpler problem than trying to solve, but have a feeling once get the methodology I can apply it to the harder problem. Let $H(p)= -q \ln(q) - p \ln(p)$ be the entropy of the Bernoulli ...
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Estimating conditional probability of bernoulli data

Assume I have $i=1,\dots,N$ fathers, each with $j=1,\dots,n_i>0$ sons. Now there is a binary event $A_{i,j}$ with outcomes 1 and 0 and the respective probabilities $p$ and $1-p$. Now I want to ...
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Accounting for non normality

I have a random variable, supposedly from a Bernoulli distribution, and I want to do some tests on its mean. I'd like to assume that the sample mean is normally distributed, but I'm not sure how ...
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Estimating the true distributions from a sample of distributions

I am having a hard time formulating the following problem. Consider a company that runs a survey across several cities in the US to estimate the percentage of right-handed people and left-handed ...
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Expected number of tosses till first head comes up

Suppose that a fair coin is tossed repeatedly until a head is obtained for the first time. What is the expected number of tosses that will be required? What is the expected number of tails that will ...
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Constructing hypothesis tests and error statistics for a bernoulli distribution

I'm trying to use a bernoulli distribution (which seems simpler than a normal distribution) to get a grip on the basic construction of hypothesis tests. So, we have a coin. Its probability of ...
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Linear combination of discrete variables $T_i$ with $P(T_i=1)=P(T_i=-1)=1/2$

Let $T_1,...,T_n$ be iid with a Rademacher distribution; i.e., $P(T_i=1)=P(T_i=-1)=1/2$; and let $w = (w_1,...,w_n) \in \mathbb{R}^n$ without further constraints on $w$. Is there a way to compute ...
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Sample size needed to estimate probability of “success” in Bernoulli trial

Suppose a game offers an event which upon completion, either gives a reward, or gives nothing. The exact mechanism for determining whether the reward is given is unknown, but I assume a random number ...
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Fisher information matrix determinant for an overparameterized model

Consider a Bernoulli random variable $X\in\{0,1\}$ with parameter $\theta$ (probability of success). The likelihood function and Fisher information (a $1 \times 1$ matrix) are:  \begin{align} ...
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When to use a normal approximation of a Bernoulli distribution

What is a practical example where one would want to use a normal approximation of a binomial distribution over using properties of the binomial distribution itself? I.e if I already know that the ...
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Text Classification using TfIdf and Bernoulli NB

So, as I am reading about Bernoulli distribution and text classification, I want to understand how Bernoulli uses TfIdf features? Since TfIdf values are within [0-1) but Multivariate Bernoulli assumes ...