# 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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### Calculating prediction variance from JAGS model of a bernoulli outcome in R

I have a model of a bernoulli random process I fit using JAGS via the rjags package in R. Here are some example data, as well as code to fit the given models in ...
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### Calculating conditional probability in Bernoulli mixture model

I'm following the book Pattern recognition and machine learning by Bishop on Bernoulli mixture model, and trying to code it. But I don't understand how to calculate the conditional probability (page ...
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### If X is Beta distributed, what is distribution of Y: Y=1 for X>0.5 and Y=0 otherwise

Consider random variable $X \sim \mathrm{Beta}(\alpha,\beta)$ What is the distribution of $Y$ defined by $Y\in \{0,1\}$, $Y=1$ if $X>0.5$ and $Y=0$ otherwise.
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### Problem Calculating Standard Error

I have a set of individuals categorized into two classes as follows: ...
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### Bernoulli Trials and Bayes Rule for a Beta Distribution?

So I stumbled upon the following question from Peter Lee's website. Suppose that your prior beliefs about the probability π of success in Bernoulli trials have mean 1/4 and variance 1/48. Give ...
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### Conditional distribution of successes in first m independent Bernoulli trials given the total number of successes

This is my attempt: I have, so far, let $Y_{mi} = 1$ if $ith$ trial in first $m$ trials is a success and of course, 0 otherwise. Indeed, $Y_m = \sum_{i=1}^mY_{mi}$. I think this is what I need ...
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### Success of Bernoulli trials with different probabilities

If 20 independent Bernoulli trials are carried out each with a different probability of success and therefore failure. What is the probability that exactly n of the 20 trials was successful? Is there ...