Questions tagged [random]
Questions relating to (pseudo)randomness, random oracles, and stochastic processes.
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11 views
When a bivariate probability distribution can be the probability distribution of $(X_1, X_1-X_2), (X_2, X_2-X_1), (-X_1, -X_2)$
Consider a bivariate probability distribution $P: \mathbb{R}^2\rightarrow [0,1]$. I have the following questions:
(1) Are there necessary conditions on the cumulative distribution function (CDF) ...
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1answer
20 views
Generalized Polya's Urn
In Polya's urn, we have $b$ black balls and $w$ white balls at time $t$. At time $t+1$, we have $b+1$ black balls with probability $\frac{b}{w+b}$ and $w+1$ white balls with probability $\frac{w}{w+b}$...
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0answers
35 views
Repeating random choice
Let's say I have 10 shirts (A to J) and I'd like to randomly wear a different one each day.
So, the one I wore yesterday (let's say shirt J) has 0% chance of being chosen today; The one I wore the ...
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0answers
11 views
Calculating expectations of concentrated random variables of bounded-differences type
Is there a nice general way of calculating the expectation variable for which I can derive concentration bounds using the method of bounded differences?
I have seen quite a few application of the ...
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1answer
23 views
Generating Two Independent Standard Normal Variables
Image of problem
I have a problem with this explanation, the book says we can generate Y1 Y2 from X1 X2
but when we want to answer questions about the distribution of X1 X2 we take arctan which ...
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1answer
34 views
st.petersburg paradox in python
I have been trying to do the St.Petersburg paradox( the player wins 2 dollars if tail appears on the first toss, 4 dollars if heads appear on the first toss and tails on the second, 8 dollars if heads ...
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0answers
22 views
Using randomly selected points uniformly distributed on the interval (0,1) find the volume of the unit sphere
I've been given this extra credit assignment to do in Matlab, but I don't understand the question. The part that I'm not clear about is where I have to satisfy the equation x+7+z>1.
Can someone ...
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0answers
5 views
Thinning operation on a spatial binomial point process (BPP)
It is known that the thinning operation performed on a Poisson point process (PPP) results in a non-homogeneous PPP. Now, if we have a spatial BPP with N points distributed uniformly over some region ...
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2answers
30 views
Generating a random sparse hermitian matrix in Python
I'd like to find a way to generate random sparse hermitian matrices in Python, but don't really know how to do so efficiently. How would I go about doing this?
Obviously, there are slow, ugly ways to ...
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1answer
16 views
Expected value in multiple rounds
I am doing an exercise that sounds like:
The game of European roulette involves spinning a wheel with 37 slots: 18 red, 18 black, and 1 green. A ball is spun onto the wheel and will eventually land ...
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0answers
10 views
Help calculating second order distribution for a continuous stochastic process
I'm really stuck on this problem, and appreciate any help.
Problem: Let $\gamma$ be a random number, chosen with uniform probability in the interval $[0,2\pi]$. We define the stochastic process $X(t)...
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Chi-Squared (observed) formula
Chi-square distribution shows how far the observed values are from expected values. [NIST SP 800-22] (https://nvlpubs.nist.gov/nistpubs/legacy/sp/nistspecialpublication800-22r1a.pdf) employs Chi-...
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3answers
69 views
Create unique one to one number from 2 numbers
A smilar question has been asked before Create unique number from 2 numbers.
is there some way to create unique number from 2 positive integer numbers? Result must be unique even for these pairs: 2 ...
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0answers
27 views
Generate random numbers with conditions using maxima (cas)
I want to generate (multiple) random numbers from a given number class with extra conditions. (for automatic generation of exercises)
e.g.:
generate "a" out of natural Numbers which are dividible by ...
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0answers
28 views
Working out expectation of a random sample.
I have the problem:
Let $X_1, X_2, X_3, X_4$ be a random sample from a population that has
mean $μ$ and variance $σ^2$.
Find $\mathbb E[(X_1-X_2)^2]$ and hence the value of $k$ such that $T
...
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2answers
41 views
Two aspects of randomness
Consider a random sequence of integers
1, 4, 3, 8, 2, 5, 3, 8 ...
The only sufficient condition for the sequence to be random is its unpredictability ie. probability of any number coming next ...
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2answers
19 views
Probability of picking 3 playing cards that belong to different suits
If you have 52 playing cards with 4 different suits (13 spades, 13 clubs, 13 hearts, and 13 diamonds), what is the probability of picking 3 random cards that are all from a different suit?
I tried ...
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0answers
10 views
What is the mean of a random number with one exclusive bound?
If I have a random number between 0 and 1 inclusive, the mean is 0.5. If both are exclusive, the distance from 0.5 to 0 and 0.5 to 1 are the same, so 0.5 is still the mean. But if 0 is inclusive and 1 ...
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0answers
43 views
Expected value and variance of random variable on some terms(dates?)
I have a exercise that sounds like this:
Find the expected value and the variance of the random variable X with natural values in terms of:
a)generating function P
b)generating function Q
Excercise ...
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0answers
34 views
Expected Length of Arc in Randomly Divided Circle.
Let's say theres a circle of unit circumference m, and the circle is divided by k points all placed randomly. The points will divide the circle up into arcs. What is the expected length of any arc in ...
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1answer
65 views
Why does the Monte-Carlo Method Work?
I've been reading about the Monte-Carlo Method and how it is much simpler for computers to use the Monte-Carlo Method to guesstimate solutions to complex problems like the Standard Model. It is ...
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0answers
11 views
Probability - Similarity Rate in the random Signal
I have a random signal (vector) that consists of random variables varying between -2 and 2. I want to know how many similar patterns do I have in this random signal. In order to achieve this, I select ...
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0answers
4 views
Can a sum of lagged variables random process be a Markov chain
Consider the following random process:
$X_0=0$, $X_{t+1}=X_t+Z_tZ_{t-1}...Z_0$ for $t\geq0$, where $Z_t$ are i.i.d. random variables with normal distribution.
In this process: $Z_0=X_1$, therefore ...
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0answers
31 views
Generating vector inside a $n$-sphere
I want to generate k n-dimensional vectors which are all inside a r-radius n-sphere and the most important : I want something uniformly distributed inside the n-sphere.
My initial idea is to generate ...
2
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1answer
51 views
What would be the chances of solving a standart 3000 piece puzzle completely at random?
I LOVE puzzeling, but this one question always bothered me. And for that I am not good at maths, I couldn't really work it out.
Here is the problem:
Say I have a 3000 pieces puzzle and I blindfold ...
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1answer
46 views
random walk with finite range
Let $X=(X_n)_{n \in \mathbb{N}}$ be a sequence of i.i.d. $\mathbb{Z}$-valued random variables satisfying the following conditions:
a) For all $n \in \mathbb{N}$ and $k \in \mathbb{Z}$, we have $\...
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votes
1answer
23 views
Counting tree nodes that end probabilistically
Suppose we have $N$ root nodes that can branch into $N$ new nodes every level. There is a maximum of 64 levels. However, on any given step, each node has a chance $P$ of terminating. What is the ...
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0answers
5 views
Soft Question: Concept of Density of a Poisson Point Process (PPP)
Consider the following code:
lamda= 0.00001
AreaR=3*10^3;
M= poissrnd(lamda*AreaR^2);
Is the generated PPP of density lamda...
1
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1answer
43 views
Probability and Computer science question
We are given a function rand() that returns a random number from the segment [0,1],
how can we use this function to create a size $100$ uniform array,
of exactly $50$ $0's$ and $50$ $1's$.
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1answer
27 views
When is an i.i.d Bernoulli Process indepent increment?
I was reading anarticle that i.i.d bernoulli process are markov and independent increment process are markov too.
So, I was wondering if an i.i.d. bernoulli process can be independent increment.
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1answer
16 views
Is the product of two random variables finite if the expectation of the random variables squared is finite?
If $E X_t^2 < \infty$ and $E Y_t^2 < \infty$, then is $E X_t Y_t$ finite?
I am thinking yes, because of Cauchy-Schwartz, since $E X_t Y_t - E X_t E Y_t$ is an inner product, so it's less than ...
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1answer
40 views
True random generation given radioactive entropy
I have been reading various sources for experimentation with truly random numbers. As I understand, it is impossible for a computer to generate a "truly random" number as they are deterministic in ...
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1answer
28 views
How to form an equation for probability based on the following graph?
The y-axis is the probability density function of x( a continuous random variable).
Here's the solution I tried:
Is this correct?
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1answer
29 views
Generating 5 random numbers less than 100 that add up to a number, 180 for example
I have found an answer (this) showing how to generate random numbers that add up to a number, but I need those numbers to be less that 100. How might I go about this?
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0answers
16 views
Identifying bias from constraining CSPRNG output
Let's say I have a sequence of random numbers between $0$ and $1$ given by $[x_1, x_2, \dots, x_n]$ from a CSPRNG. The distribution is uniform.
Now I permute my random numbers such that it follows a ...
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1answer
17 views
Balls and Bins problem max size of bin
I need to make a program which satisfies the below (my question is not about code):
The Balls’n Bins-problem deals with the experiment of randomly distributing a number of balls into an equal ...
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0answers
22 views
Randomized Submatrix of a Sparse Matrix
I have a sparse square matrix $A$ with size $n \times n$ and number of nonzero entries $nnz$.
The goal is making a sub-matrix $B$ with $s$ nonzeros which are randomly chosen from $A$. Duplicates are ...
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1answer
110 views
Let X be distribution over N (the set of non-negative numbers), with mass P(X=i) = a/2^i, what is the value of a?
I am struggling with solution for following problem part of course about probabilities random variables, seek your kind help to show how to solve it,
Let $X$ be distribution over $N$ (the set of non-...
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0answers
8 views
Sample from random normal with sliding mean
I have a uniform random variable $x$ and a normal random variable $z = \mathcal{N}(x, \sigma)$ (i.e. the mean is given by $x$). How can I draw samples $(X, Z)$ such that they correspond to their ...
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0answers
25 views
The independence of two random uniform distribution random variables
$y_1 = x_1 + x_0$;
$y_2 = x_2 + x_0$.
Suppose that $x_1$, $x_2$, and $x_0$ are independent with each other. They all follow the uniform distribution in $[0, 1]$.
Then, I want to know if $y_1$ and $...
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0answers
28 views
Random walks in different directions?
Assume a person random walker takes equal steps to the right or left with equal probability.
Probability that taking n steps, the person walking will be displaced 1 standard deviation or greater in ...
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2answers
61 views
How many roots exist for $y=sec(x)$
In the interval $( - \pi ,\ \pi ]$.There are 2 roots exist mentioned in the book. Could anyone please explain how?
Exact question from book : Let $Y=\sec X$ .Compute $f_Y(y)$ in terms of $f_X(x)$ ....
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2answers
26 views
Simulate a discrete random variable
We have a discrete random variable $X$ with the following probability distribution
\begin{equation*}
p(X=i)=p_i,\quad i=1,2,\ldots 1000, \quad \sum_{i=1}^{1000}p_i=1.
\end{equation*}
How we can apply ...
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2answers
22 views
Probability of having a link in union of Erdos Renyi random graph
We have two Erdos-Renyi random graphs, $G_1$ and $G_2$, generated with probability $p_1$ and $p_2$, respectively.
If we take the union $G_1$ $\bigcup$ $G_2$, we obtain another Erdos-Renyi graph, $G_3$...
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1answer
19 views
probability after ten draws
I would like to know if my partial solution is appropriate:
We have ten urns, in each urn we have 2 balls:
in 1st urn - 2 balls of number 1
in 2nd urn - 2 balls of number 2
.
.
in 10th urn - 2 ...
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2answers
50 views
Question on Random Variables from the textbook “Mathematical Statistics and Data Analysis” by John Rice
If $U$ is a uniform random variable on $[0,1]$, what is the distribution of the random variable $X=[nU]$, where $[t]$ denotes the greatest integer less than or equal to $t$?
I've tried searching ...
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0answers
18 views
Connections between the randomness of the normal distribution and Textrank?
In a TED speech on 8:40 the mathematician said that:
This algorithm uses the laws of mathematical randomness to determine
automatically the most relevant web pages, in the same way as we used
...
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1answer
38 views
Probability two sequences of coin flips reach consecutive heads at the same time.
Two people start flipping coins. The probability of heads is 0.5 (bonus if you can do it for $p_1$ and $p_2$). What is the probability that both will hit two consecutive heads simultaneously (as ...
4
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1answer
74 views
Sum of Uniform(5,10) random variables to get more than 30
Let $X_i$ be i.i.d. $Uniform(5,10)$, and let $Y_t = \sum_{i=1}^t X_i$. Let $T = \mbox{inf}\{t:Y_t \geq 30\}$, what is $\mathbb{E}[T]$?
At first I thought this was similar to Choose a random number ...
3
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1answer
52 views
Reachability of points on Manifolds
I was thinking with a friend that on a surface some points are more reachable than other.In the sense that their average distance to the other points is lower.
e.g. suppose that we have a circle in a ...
