Questions tagged [random]

Questions relating to (pseudo)randomness, random oracles, and stochastic processes.

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What do these operations mean? $A ∩ B$ or $ A ∪ B$ or $A^c$?

To be more specific; What does it mean when I read my book: $A ∩ B = (2, 4) $ ? What does this say about A and B? How are they related? Same with: $A ∪ B $ and, $A^c$ , where c is a complement operator??
Math420
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Is Brownian motion random or haphazard?

According to Wikipedia https://en.wikipedia.org/wiki/Randomness, randomness is a measure of uncertainty of an outcome, rather than haphazardness. I was wondering if the Brownian motion is an example of haphazardness. If not, is there another…
pavybez
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Let $(X_n)_{n \in N}$ be a Markov chain with the set of states $I=\{ 0,1,2,3\}$ and with given transition matrix.$P\{ X_5=1, X_3=1, X_2=3| X_1 = 2\}$?

Let $(X_n)_{n \in N}$ be a Markov chain with the set of states $I=\{ 0,1,2,3\}$ and with the given transition matrix: $$P=\begin{bmatrix} \frac{1}{4} & \frac{3}{4} & 0 & 0 \\ \frac{1}{2} & \frac{1}{4} & 0 & \frac{1}{4} \\ \frac{1}{3} & 0…
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Expected value of $\max\{0, \text{Tails}-\text{Heads}\}$

Let suppose I flip a biased coin (infinite number of times), and at any given time I'm interested in the difference between T and H, that came up until now. (but not really) I want to have $\xi_n$ - to be the flip result ($-1$ for heads with…
dEmigOd
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select a randomly chosen subset of integer range

I tried to ask this question on stack overflow, but it was not well received. I want to generate an ordered sequence of finitely many random integers in a range such that any N-element subset (having no duplicates) of [b,e] is equally likely. To do…
Jim Newton
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If x, y, and z are random numbers from 0 to 1, what is the probability that x+y+z<1?

If $x$, $y$, and $z$ are random numbers from $0$ to $1$, what is the probability that $x+y+z<1$? I know that the answer is $\frac{1}{6}$ but I am not sure how to get there. If this problem had two variables, I could graph $x+y<1$ and look at the…
shurup
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Non-immediately repeating random sequence -- terms / concepts

Supposing I have a fair die and record the rolls, but ignore and reroll any immediate repeats. For example, I roll: 3 2 1 (1) 5 6 (6) (6) 3 1 And I record: 3 2 1 5 6 3 1 ...and so forth, ignoring (1) and (6) (6) and…
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Probability of finding different ball in two box random

Assume that we have 2 boxes each contains 5 balls , there is one ball among all these ball that is different from other balls , we want to choose 3 ball randomly from each box ( we will put the ball back after checking whether its the one or not ) ,…
Mahan
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Random variable over a random binary sequence

is it possibile to construct a random variable such that the avarage of its values matching 0s in a binary sequence is double than its values matching 1s? For instance given a binary random sequence of 0s and 1s assign to each value of the sequence…
francesco
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Showing that $3/4$ of all words over $\{0,1\}^n$ have $K(w) \geq n-2$

$K(n)$ is the kolmogorov-complexity of a word n. I know that for every $n$, there's at least one word $w_{n}$ of length $n$, such that $k(w_{n}) \geq n$. There's $2^n$ words in $\{0,1\}^n$, how can I continze from here?
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Proving that at least half of all words with length bigger than $n$ are not compressible.

We say that a word is not compressible, if it's Kolmogorov-Complexity is bigger than the length of the word. We know that for every natural number $n$, we have at least one word which is not compressible. How can I now show that at least half of all…
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How do you randomly select unit grid boxes non uniformly from a rectangle?

I have a task to do with random numbers . What I have is a rectangular grid of dimension $i \times j$. This grid is subdivided into $ij$ unit boxes $1 \times 1$ each . Say just like this. Now I have to randomly select these unit boxes such that I…
Shivam Patel
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How much randomness is in human-generated random digit string?

Suppose someone is asked to provide a long string of random digits, for example: 4866710938572235108576927175549668592830123185576923856998372006958477486523 (just typed on keyboard, not generated in any way) How good is it expected to be if used…
Vi0
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Expectation on the product of two random processes

As the title said, how to calculate the expectation on the product of two random processes as follows: $E\left[R(\mathbb{x})R'(\mathbb{x})\right]$, where $R(\mathbb{x})$ and $R'(\mathbb{x})$ represent two different Gaussian processes, and…
user22986
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Quality of presudorandom number generator

I have to test the quality of the pseudorandom number generators on the different samples. I understand that the good way is to select dispersion as a quality metrics. I'm trying to find dispersion using the following…
Rahul
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