# Questions tagged [probability]

A probability provides a quantitative description of the likely occurrence of a particular event.

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### Goodness-of-fit test for very skewed data [closed]

I am working with two quite large datasets (9000 obs and 3800 obs). Each observation has been grouped into 1 of 12 categories and I am looking to test if the frequency of categories in the smaller ...
1 vote
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### Likelihood ratio as minimal sufficient statistics in infinite parameter space

I just read a question from here (Likelihood ratio minimal sufficient) and have some thoughts. Let me restate the question first: Consider a family of density functions $f(x|\theta)$ where the ...
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### Convergence in product of sequence of random variables

This question has been addressed previously in here but my question is different. It is from Hogg and McKean's "Introduction to Mathematical Statistics". Theorem $5.2.7.$ Let $\{X_n\}$ be a ...
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### Group aggregates of conditional probabilities

I suspect I don't know the academic or SEO word for what I'm looking for. Put simply, I want to know a group's total expected success rate given each member's likelihood of attempting the "trial&...
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### drawing from multiple urns based on a random number

Suppose I have $N$ numbered urns, each with different colored balls. Now I have some fixed discrete distribution that I use to draw a random number $i \in \{1 ... N\}$. I now pick a ball from urn $i$, ...
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### Random walk on cube with condition of not returning

An ant is placed in a corner of a cube and cannot move. A spider starts from the opposite corner, and can move along the cube's edges in any direction (x,y,z) with equal probability 1/3. On average, ...
1 vote
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### Likelihood of sum of log-normal and normal distribution [closed]

Given $y(x_t)=e^{f(x_t)}-\varepsilon _t$ with $\varepsilon _t\sim N(0,4e^{f(x_t)})$ and $f\sim GP(\mu,\sum)$. What is the likelihood $p(y|f)$? Is it $p(y|f)\sim N(e^{f(x_t)},4e^{f(x_t)})$? Thanks a ...
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### Bayes's theorem problem issues

Problem Statement: Assume that 40% of all interstate highway accidents involve excessive speed by at least one of the drivers (event $E$) and that 30% involve alcohol use by at least one driver (event ...
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### Question about mean hitting times

A homogeneous Markov chain $\{X_n\}_{n\in\mathbb N}$ with discrete state space $\mathcal{S}$. Set $$\tau_{k}:=\text{inf} \left\{n\ge 0:\, X_n=k \right\}.$$ where $\tau_{k}$ is defined to be $+\infty$,...
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### Expectation propagation: $g_i(\theta)\sim\mathcal{N}(\mu_i,\Sigma_i)$ but $\Sigma_i^{-1}$ is non-invertible

I paste here the section on Expectation Propagation from Gelman et al.'s Bayesian Data Analysis (pg 340). I have two questions: In Step 5 (with the red box), where we infer the hyperparameters of the ...
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1 vote
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### how to assess how likely it is that a candidate gets more than 50% of the total votes [closed]

So far in a country are counting votes and 72.9% of the votes have been counted. Candidate A has 43.8% of the votes, candidate B has 43.54%. Assuming that there are not a significant difference ...
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### Best rigorous book on probability theory for ESL [closed]

I know this is similar to many questions asked here before, but I couldn’t find question that addressed what I need. I started ESL but I’m having a lot of trouble with the probability theory part of ...
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