# Tagged Questions

This tag is for basic questions about probability and for questions in which one wants to calculate a probability, expected value, variance, standard deviation, or similar quantity. For questions about the theoretical footing of probability (especially using measure theory), please ask under (...

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### random variable follows

I have a random variable $x_1$ that follows the normal distribution with mean 0 and variance 1 with probability 0.6 and follows the normal distribution with mean 0 and variance 2 with probability 0.4. ...
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### How can I prove it?! [duplicate]

let $X$ and $Y$ be two independent RV with the same distribution. Prove that: $$P\left(|X-Y|\le 2\right)\le 3P\left(|X-Y|\le 1\right)$$ I was wondering if you help me.
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### If $(\xi_k), k \ge 0$ is a sequence of iid Gaussian variables, does it hold a.s. that $\sum \xi_k^2 = +\infty$?

I think that the probability is either 0 or 1 by Kolmogorov 0-1 law.
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### Proving how to reduce a Brownian walk on a plane to a line (2D to 1D)

I have a Brownian motion on a plane and would like to find the time of when it is expected to hit a set of parallel lines, i.e the hitting time. In order to do so, I understand that I can reduce the ...
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### Jar containing 80 balls. 40 red and 40 black.

The jar contains 80 balls. 40 are red and 40 are black. We pick 20 balls out of the jar without putting them back. What is the probability that 10 out of 20 balls will be black and the other 10 will ...
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### Pearson correlation of neural responses with it's linear estimation

I am trying to anderstand the following fact: Suppose I have a linear estimation of a stimulus: $\hat{s} = \mathbf{w}^T(\mathbf{r} - \mathbf{f}(s_0)) + s_0$ where $\mathbf{w}$ is a vector of ...
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### How to become very good in probability and combinatory [closed]

How someone become very good in probability and combinatory? Is there is a set of methods used to solve problems in this field? If you can suggest any resources or tips to improve myself in this ...
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### Approximating statistics for huge dataset

I'm investigating users accounts statistics for Vkontakte social network. There are $N\approx2 \cdot 10^8$ accounts that have different metrics along them – boolean, discrete and continuous. I found ...
### Markov DTMC and CTMC: How to build a $Q$ generating matrix using given $2$ state $q$ probabilities? Find Steady State Probabilities
I know that $$q_{(i,j)(i+1,j)}=\lambda_1$$ $$q_{(i,j)(i-1,j+1)}=\lambda_2$$ $$q_{(i,j)(i+1,j-1)}=0.5\lambda_3$$ $$q_{(i,j)(i,j-1)}=0.5\lambda_3$$ where $\lambda_1 , \lambda_2 , \lambda_3$ are rates ...