# Tagged Questions

The probability that an event A will occur, when another event B is known to occur or to have occurred. It is commonly denoted by P(A|B).

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### Finding conditional probability of getting a number on a die and Jacks in Hand

Suppose we roll a fair six-sided die and then pick a number of cards from a well-shuffled deck equal to the number showing on the die. (For example, if the die shows 4, then we pick 4 cards.) (a) ...
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### How to draw a conditional distribution graph for B given A

Below is a frequency table which has data for testing a theory that students who speak a foreign language are also strong mathematics students. The question says to draw a graph showing conditional ...
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### conditional probability results in value greater than 1

I am not an expert in probability theory so please bare with me. Suppose I have a one sentence corpus as follows: How to go about it It's quite obvious to see that the corpus has 5 words. Here is how ...
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### Conditional independent Poisson variables modelling count data

A study question I have been looking at for sometime has confused me somewhat. I have conditionally independent Poisson count observations with a hierarchical structure to the data. The format of ...
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### Confusion regarding conditional distirbution of the product of gaussian process with a normal

I am getting confusedregarding a simplae problem. say $Y = WX$ where $X$ is a q X n matrix with each row a Gaussian process denoted as $\mathcal{GP}(M(\mathbf{X_i}),C(\mathbf{X_i},\mathbf{X_i}))$, in ...
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### Conditioning within definition explanation

I have a doubt on the meaning of a conditioning within a definition. In a book I've found the following definition of upper tolerance limit: $P(P(X<\bar X+kS|\bar X, S)>p)=1-\alpha$ where $X$ ...
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### What is the probability of the first positive event in an sequence of binary events where sequences have finite but random lengths?

I have a time series of observations from a longitudinal study of individual objects. These observations are seen as discrete sequences of features, one sequence per object. The sequences have ...
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### Gibbs Sampling for LDA example

Can someone provide an example of 1 (or more) iteration(s) of Gibbs sampling for LDA using real values? I have been searching for a while and I can't seem to find any good examples. Thank you.
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### number of parameters for a Bayesian network over binary random variables

I am working through the exercises of a book (Bayesian Reasoning and Machine Learning) for machine learning but I got stuck (I do not understand the question). The following three variable ...
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### Conditional expectation of a univariate Gaussian

Suppose I have a univariate Gaussian distribution with mean $\mu_X$ and standard deviation $\sigma_X$, and I know the random variable $X$ is least some positive value $y$: $X \geq y$. What is the ...
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### I need help with this stat problem [duplicate]

A friend claims that because there is a 50% chance for a coin to land on heads, the fact that the last three coin flips landed on tails means that there is a higher chance for the coin to land on ...
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### intuitive difference between joint probability and conditional probability in this example

I was reading a tutorial on marginal densities when I came across this example (rephrased). A person is crossing the street and we want to compute the probability when he gets hit by a passing car ...
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### Understanding statistical independence of events using a relative frequency interpretation

This is what I've read in my textbook: "If $n_A$ and $n_B$ are the number of times the independent events $A$ and $B$ have occurred, then we expect that the ratio $\frac{n_{AB}}{n_A}$ (num. of times ...
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### Sampling from marginal distribution using conditional distribution?

I want to sample from a univariate density $f_X$ but I only know the relationship: $$f_X(x) = \int f_{X\vert Y}(x\vert y)f_Y(y) dy.$$ I want to avoid the use of MCMC (directly on the integral ...
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### Probability of receiving each preference in an internship drawing

I have to write a 23 itens preference list of places where to perform my internship. There will be a lottery which I don't know how exactly they will weight the preferences to distribute us. The ...
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### In a markov chain, how to deal with final states that are not in the initial states - Probability of Default

I'm analyzing a bank portfolio in order to determine the consequent probability of default using markov chains. For this I select the group of credits at the end of month 'n' and measure their credit ...
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### Forming distribution conditioned on many variables from single conditional marginals using copulas

I'm brainstorming about a data analysis project, part of which can be thought of as estimating a joint distribution from marginals, so I'd like to know whether I can use some copula techniques. ...
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### What are the differences in linearity in Non-stochastic and Stochastic Regression?

I have been confused with the difference/distinction between stochastic and non-stochastic explanatory variables for while. I was able to write down my current understanding some time ago and am ...
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### Specifying conditional probability tables for nodes with large number of Parents in a Bayesian Belief Network

What is the ideal way to specify the conditional probability tables for belief propagation in a Bayesian Network, for nodes with large number of parents? I am currently using gRain package in R. But ...
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### Naive Bayes and smoothing

For simplicity, let's say that we want to perform binary classification using Naive Bayes on a Boolean function. That is, the target function is $c: \{0, 1\}^n \rightarrow \{0, 1\}$. Hence, the two ...
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### I need someone to check my conditional probability calculation function

I am following the book "Think Stats. Probability and Statistics for Programmers" and doing the exercises using numpy + pandas. Currently I am on exercise 2.7 on conditional probability: Exercise ...
Problem Setup Let $\{X^d_1, X^d_2, \cdots, X^d_n\}$ be a $d-$dimensional zero-mean, i.i.d. random variables. Let $S_n^d$ be $$S^d_n = \frac{\sum_{i=1}^n X_i^d}{\sqrt{n}}$$ Let $Y^d$ be a zero-...