# Questions tagged [probability]

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

7,000 questions
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### Observational Data and Bias - A real problem

I'm hoping you all can provide some guidance. I'm working a problem with the following objectives and data set. I would like to be able to predict, for each unit, at each sampled moment, the expected ...
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### Scikit-Learn Gaussian Mixture: How can log-probabilities be positive? [closed]

I am fitting a Gaussian Mixture model: gm = GaussianMixture(n_components=K) gm.fit(features) When I do: ...
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### Distance between two distributions

I am analyzing time-series data, and I would like to detect a significant change in data distribution. I already know about Bhattacharyya distance, but that requires histograms of equal-sized bins. ...
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### Non Linear transformation of Random Variable

I have a pdf say $p(x)$. Now, I apply some transformation (may be linear or non-linear) to the variable $x$ say $g(x)$. Let the new pdf be called $p(y)$. For, a small change in $x$ say $dx$, there ...
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### X is Uniform $[-\theta,\theta]$ what is the distribution of $Y=\frac{1}{x^{2}}$?

X is Uniform $[-\theta,\theta], \theta>0$ what is the distribution of $Y=\frac{1}{x^{2}}$ So I've been working on some transformation questions; however, most of them have been one to one. I am a ...
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### How to combine confidence and probability scores into a single metric

I have an algorithm which outputs a confidence score and a probability score that a particular user belongs to class $C_i$, for multiple values of $i$. I want to output a single class $C_o$ as the ...
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### Confusion about the probability of being dealt 2 pairs

There are seemingly three ways to calculate this, and they yield different answers. Please help me understand which way is correct. 1) Having two pairs is choosing 2 ranks (namely A and B) out of 13 ...
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### Probability distribution for draws with conditional replacement? (or how many matches does it take to beat Yugi The Destiny?)

While trying to figure out an old video game, I seem to have stumbled upon a problem that's halfway between a binomial distribution problem and a hyper-geometric distribution problem. With the hopes ...
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### Updating the odds / probability once user plays a bet

I am working on an assignment in which I have created a game in which user will bet on outcome of a game. Team A will win or not. if win = Invest 7 get 10 if not win = Invest 5 get 10 I have an ...
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### Find $P(A^2 < B)$ where $A$ and $B$ are independent and uniformly distributed $\mathrm{Unif}(0,h)$, $h > 0$

I solved it two ways and in both the cases the answer is different and different from the actual answer. Approach 1: Since, $A$ and $B$ are independent, we can find the joint distribution of $AB$ ...
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### Estimate expected power on a wind turbine based on other nearby wind turbines

I'm looking for a reliable way to estimate the power that a wind turbine should be producing, based on the power that its neighbours are producing. We use this to identify turbines that are ...
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### Mass of single random variable from joint mass

I'm taking a course on probability and confused about single variable mass and joint mass. Here is a quote of the video, I'm learning from: Using the joint mass to calculate the mass of a single ...
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### Transformation of Random Variables and making sense

So, I was going through Pattern Recognition and Machine learning by Bishop, page - 18, and I came across probability densities where I read about the transformation of a random variable. I couldn't ...
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### clarification on Bayes theorem application

I'm experimenting with bayes rule. I have been invited to last stage interview in highly selective company. I want to use bayes rule to evaluate my chances of getting the post. Let's define the ...
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### Probability that at least 3 of the 5 randomly selected questions can be solved

As my friend my studying for her final for her Philosophy class, she asked me a question. The professor assigned a list of 10 essay questions, and would be picking 5 to put on the exam. Of the 5 ...
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### How is probability y = j|X calculated from an ordinal logistic regression model?

I have an ordinal logistic regression model fitted with lrm from the rms library in R, and am presenting results as prob y = j|X ...
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### Sufficient Conditions for the Central Limit Theorem

My understanding is that the central limit theorem applies as long as the variance of the random variable is less than infinity. Is this equivalent to saying that all moments are finite? If not, what ...
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### Minimum of n independent, but not identically distributed inverse Gaussians

I would like to find the probability distribution of n independent, but not identically distributed, i.e. differently parametrized inverse Gaussians. I would prefer an analytical solution. Also, would ...
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### Covariance of Two Quadratic Forms

We're looking for the $\operatorname{Cov}\left[x^T A x, ~x^T B x\right]$ where $x$ is random variable and mean-centered, but not independent and $A$ and $B$ are symmetric matrices. The fundamental ...
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### Who invented the independence notation $\perp \!\!\! \perp$?
This is more of a historical question: who invented the notation $\perp \!\!\! \perp$ for denoting (conditional) independence?