# Questions tagged [probability]

For basic questions about probability and for questions about calculating a probability, expected value, variance, standard deviation, or similar quantity. For questions about the theoretical footing of probability (especially using [tag:measure theory]), ask under [tag:probability-theory] instead. For questions about specific probability distributions, use [tag:probability-distributions] instead.

67,666 questions
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I just learned about the Monty Hall Problem and it seemed pretty much amazing to me.I am just a bit confused with it. So,according to the problem we are on a game show, and we are given the choice of ...
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Suppose that we have PN objects (disks for an example) and we have P slots (or boxes),how many ways can we distribute those PN objects on those P slots so that each slot has exactly N object? i saw a ...
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### Do jumps in Levy processes need to be independent of the process itself?

I have a very basic question about Levy processes. Is the process of the form $$X_t=\sigma (X_t) B_t + \sum_{i=1}^{N_t}\eta_i(X_t)$$ a Levy process? Here $B_t$ is a standard Brownian motion and $N_t$...
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### Counting process which is not a Poisson process

Please construct a counting process N, whose r.v. N(t) are distributed as Poisson(λt) but the process N itself is not a Poisson process. This is an assignment in our Stochastic Process class. So I ...
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### How do you determine if a pair of random variables are independent?

If $A$ is a subset of $R$ and $X$ is a random variable. I have two variables $X_1$ and $X_2$. $I$ being $1$ if $X$ in subset $A$ and $0$ if not in $A$. Let $U$~$U(0;1)$ and determine if this pair ...
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### Expected Entropy Based on Dirichlet Distribution

The Dirichlet Distribution basically defines the probability that a sample came from a particular multinomial distribution if we assume that the prior probability of all multinomial distributions ...
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### How to understand this probability equation?

$\mathbf { x } ( t ) = g ( \mathbf { s } ( t ) ; \xi ) + \mathbf { n } ( t )$, where n(t) denotes the noise or modeling error and ξ the parameters of mapping $g$ How to understand the following ...
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### Expected number of random rows needed to get a full-rank matrix

I have a random $m \times n$ matrix over $F_2$ of full rank (i.e. all columns are independent) where $m$ << $n$. Now, I wish to randomly choose $k$ rows such that the corresponding sub-matrix (...
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### Joint Exponential Probability Problem

I have a question from A First Course in Probability by Sheldon Ross. Question: Consider two components and three types of shocks. A type 1 shock causes component 1 to fail, a type 2 shock causes ...
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### Probability the event occurs knowing that I received no information

First I want to thank you if you pay attention to my post. I apologize if it seems elementary to you, note that I searched a lot an answer before posting. I'm going to try not to be vague, do not ...
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### What is the probability of drawing 2 same colored marbles?

Suppose there are 3 colored marbles (Red, Blue, Green). There are 10 red, 20 blue, 30 green marbles. You select 2 marbles without replacement. What is the probability that they are the same colors? ...
### $\exp(-t^4)$ is not a characteristic function
A communication network is made of nodes conected with wire. The net sends packets in such a way that if one packet is located in an internal node $x$ (internal node is the one connected to more than ...