# Questions tagged [probability]

For questions about probability. independence, total probability and conditional probability. For questions about the theoretical footing of probability use [tag:probability-theory]. For questions about specific probability distributions, use [tag:probability-distributions].

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### Probability mass function for combinatorics problem

The question is as follows: A small pond contains 15 fish: 10 blue fish and 5 red fish. A set of 5 fish are caught at random. (Once a fish is caught it is not placed back in the pond.) Let K be the ...
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### Finding References for known results about mixing time of a Markov chain arising from Gaussian elimination

I am looking for references for the known results on the following problem. Let $(X_t)$ be a Markov chain on $GL_n(F_2)$, where in each step, an ordered pair $(i,j)$ is chosen uniformly at random, and ...
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### Stochastic Gaussian Process vs Non-Stochastic Gaussian Process?

Lately I have observed that there are two types of Gaussian Processes: Type 1: https://www.cs.toronto.edu/~rgrosse/courses/csc411_f18/slides/lec20-slides.pdf Type 2: https://en.wikipedia.org/wiki/...
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### Probabilities I'm gonna win a tournament when I'm better at one game and bad at another

I'm playing a game of chess and go. It's a three round game and to win I have to win two rounds in a row. I'm better at chess and my opponent is better at go. I can chose to play go-chess-go or chess-...
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### I'm quite unsure how to approach part (d). Would greatly appreciate any advice. Thanks in advance!

I'm unable to embed. Here's the link to the question
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### FOB Poker: Probability of a sequence of numbers (with the existence of "wild-card" number)

At work we have 2 factor authentication using a fob that generates a sequence of 6 numbers 0-9. We started playing "poker" by having everyone generate a number at the same time and see who ...
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### Why are logarithms used to measure Similarity?

I was reading this link on how to test the difference between 2 probability distributions :https://chjackson.github.io/kl.html. If $P(x)$ and $Q(x)$ are discrete distributions, the KL Divergence can ...
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### What is the meaning of $p_{g_i}$ in this equation?

I am reading "The element of statistical learning" and having some question regarding equation 2.36. The book stated that: "A more interesting example is the multinomial likelihood for ...
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### Evaluating $\lim_{n\to \infty} \frac{1}{n}\int_0^n \max(\{x\},\{\sqrt{2}x\},\{\sqrt{3}x\})dx$, where $\{x\}$ is the fractional part of $x$

I found an interesting problem on the internet: $\lim_{n\to \infty} \frac{1}{n}\int_0^n \max(\{x\},\{\sqrt{2}x\},\{\sqrt{3}x\})dx$, where $\{x\}$ is the fractional part of $x$. I have known that this ...
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### Counting squares in a regular polygon with $4n$ vertices ($n \geq 2$)

Select at random $4$ vertices from a regular polygon with $4n$ vertices ($n \geq 2$). Find $n$ providing that the probability that the $4$ chosen vertices are the vertices of a rectangle that is not a ...
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### Want an example of uncorrelated but dependent joint Bernoulli example [closed]

Can anyone give an example (joint probability table) that two Bernoulli variables are uncorrelated but not independent?
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### What does it mean that the mean squared error of a test data is smaller than the training?

I was working with a set of data. I used bayesian regression to derive a model for it and I get the following results. MSE for bayesian regression testing data : $0.14611199672315536$ MSE for bayesian ...
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