Questions relating to (pseudo)randomness, random oracles, and stochastic processes.
Questions tagged [random]
1860 questions
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Random walk in nXn grid. probability reaching top row
A woman walks randomly on a nxn grid starting at the point (1,1) (the lower left corner). Each minute the women moves either to the right or up (so (a,b)-> (a+1,b) or (a,b)->(a,b+1). Her walk ends when she reaches the upper right corner, at the…
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Finding derivative of this integral function.
I need help on finding the derivative of this:
$$g(x) = \int_1^{x^2} (x-t)\sin^2(t)dt$$
I thought about taking out x and having it as a constant but how?
Kenneth
- 79
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Pseudo random ordering of integers
I remember an old retro effect for a screen resolution of $320\times 240$. You would iterate the pixels in a linear fashion so there are $76800$ pixels. You could iterate then one by one starting at pixel $0$ and ending with pixel $76800-1$.…
vidstige
- 123
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Exercise from probability
In normal deck of cards each of the cards have some rank (2 have rank 2, 3 have rank 3, ... , J have rank 11, Q have rank 12, K have rank 13 and A have rank 14). 3 cards are drawn. We have the random variable X which gives us the absolute difference…
user112506
- 3
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Given a Sum, How to Randomly Generate Variables
I have five variables:
A=2
B=3
C=4
D=5
E=6
I want to create a random array of these variables so that their sum equals a given number X.
Example if X=21, a possible output would be {D,B,A,D,E}. Note that variables may be used more than once or not…
parap
- 119
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1 answer
Prove that this is a legitimate PMF
I know that these are two properties of PMF.
Non-negativity
Sum over the support equals 1
However I can't show that this PMF's sum over the support equals 1.
Muon
- 35
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E(Xn)=infinity implies p-lim(Xn/n)=0?
I am struggling with an exercise… the first part of the exercise was ok, but the second part is a lot less trivial.
$X_n$ are non negative iid random variables.
First part: check that if $E(X_i)$ finite then $\lim X_n/n=0$ almost surely. I showed…
JenniferK
- 19
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Determining the best seed for a PRNG to approach a value
Is there a practical/realistic way for a Mersenne twister (or another PRNG, if you deem it more appropriate) to have their seed selected to approach a 10MB large number as close as possible in less than 20 seconds on modern hardware?
So one would…
Kroma
- 119
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Linear Congruential Generator has toggling lowest bit?
I am learning about linear congruential generators and read a page at the Lawrence Livermore web site about it. It says the following is a good LCG random number generator:
$$
x[n] = a x[n - 1] + b (mod2^{64}), a = 2862933555777941757, b =…
Anopt
- 101
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Would this method yield a truly random sequence?
A creates some content A, say a poem. He assigns an arbitrary number value to each letter of the alphabet. He then selects a random piece of content B somewhere on the web without analyzing it. The first letter of that content is then shifted…
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How to use the Inverse Transform Method to generate samples from f(x)= 1/12* 3√ x where 0 ≤ x ≤ 8
I am trying to use the Inverse Transform Method to generate samples from this equation 1/12 * cube root of x where 0<=x<8. I have tried following some of the tutorials on the site with no success, please help me. I am trying to revise for an end of…
TechGeek
- 101
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2 answers
How to Generate Random Mathematical Equations that Equal an Integer
Looking for a way to generate random mathematical equations that equal an integer between 0 and 9, a way to rank the complexity of the equation rendered, and a method to note the mathematical concepts utilized within the equation.
My first guess is…
blunders
- 263
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1 answer
The degree of a vertex in the grapf of a erdos graph
I have the following question: Consider a random graph on nvertices, where between any two vertices there is an edge with probability p = c/n, (alternatively, no edge with probability 1-p) all edges are independent. Using the characteristic…
Arsen
- 41
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3 color ball problem
I have essentially infinite number of balls, ⅓ each of 3 colors. How many must I blindly draw to be 95% confident I have 1 or each color? I think the answer is 11, but I'd like the equation.
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Generating distinct random numbers from uint256 in range
My goal is to generate around 1500 distinct random numbers, from range 8000.
I receive (blockchain ChainLink VRF - connected to random oracle, but that's not important):
variable array of uint256[] randomValues: unsigned values <0, 2^256-1>
i…
wtdmn
- 43