3
votes
1answer
70 views

[Probability]need help to understand the following expression

So assume $Y$ and $X$ are exponentially distributed with parameters $y_1$, and $x_1$ respecitively. assume c is a constant. I am having huge trouble to understand the integration of the following ...
2
votes
2answers
28 views

Select an element without uniform distribution with a uniform random without iterations

I have N elements (numbered from 0 to N-1) and I must choose one but without the same probability. For example, I need that the 0 must happen 50% of times, 1 with a 25%, 2 with a 12.5%, etc. I don't ...
1
vote
1answer
34 views

Generate random numbers with a modified PERT distribution

I want to generate random numbers based on the modified PERT distribution. The modified PERT distribution is a special case of the beta distribution and is defined as: $$f_X(x) = ...
0
votes
1answer
39 views

How does a pdf of the difference of two random variables relate to the pdf of each random variable

Let $T_1$ and $T_2$ be non-negative continuous random variables (rv) denoted in the form $T_i = \mu_i + \sigma_i X_i$ for $i=1,2$ where \begin{eqnarray*} T_{1} &=&\mu _{1}+\sigma _{1}X_{1} \\ ...
1
vote
1answer
38 views

Probability Density of Convolution of Two Random Processes or Variables

Suppose that we have two stationary random processes $x(t)$ and $y(t)$ with probability density functions $f_{x}(x)$ and $f_{y}(y)$ respectively. Now suppose we form: $z(t) = x(t) \ast y(t)$ What is ...
1
vote
0answers
14 views

Raffle between different groups composed by different numbers

I've got this issue, I need to prepare a raffle between teams for a cars race. Cars are grouped by teams. Rounds are 1:1, composed by different manches until the cars are done. Total number of cars is ...
1
vote
2answers
53 views

Simple algorithm for generating Poisson distribution

I found a very simple algorithm that draws values from a Poisson distribution from this project. The algorithm's code in Java is: ...
0
votes
1answer
41 views

Given the distribution of a random variable $R$, who do you get a uniform random variable $U$?

Let us say you have a random variable $R$. How would one generate a uniform random variable $U$, with the maximum possible entropy (or infinite entropy, if $R$ has such)? (For simplicity, you may ...
0
votes
1answer
32 views

Moments of Geometric Random Variable

Let $X$ be a geometric random variable i.e. it represents the number of consecutive failures before you get the first success where the success probability is $\rho$. We know $E[X] = 1/\rho$ and ...
5
votes
1answer
186 views

Asymptotics of sum of binomial distributions

Definition 1: For any random variable $X$, we define $\mathrm{Bin}(p,X)$ as a variable with binomial distribution having parameters $p$ and $X$. Definition 2: For all $i \in \mathbb{N}$, define ...
1
vote
1answer
98 views

Solution of equation of binomial random variables

Is it possible to find the probability distribution of the random variable $X$ that solves the following equation? $$ X = Bin(X, p) + Bin(X, 1-p), $$ where $Bin(X,p)$ is a random variable distributed ...
0
votes
1answer
78 views

Generating Random Serialnumber with least similarity

I want to generate 16-digits hexadecimal serial-number like: F204-8BE2-17A2-CFF3. (This pattern give me 16^16 distinct serial-number But I don't need all of them as I describe below) I need an idea ...
3
votes
0answers
36 views

Can I solve this probabilistic problem or do I need more data?

This problem happened to me almost 3 years ago and I just discovered this site by luck, so I want some help to know if this problem is solvable (if so, I would like to know how to solve it as well as ...
0
votes
1answer
61 views

2 dimensional random walk - hit of targets

Consider a random walk in $\mathbb{Z}^2$, $x(j) = x(j-1) + \xi_j$, where the increments are random variables independent and identically distributed with finite support, the expectation $m := ...
4
votes
0answers
33 views

Entries of a Haar distributed unitary matrix

The eigenvector matrix of a Wishart matrix is Haar distributed and that implies that the eigenvectors are uniformly distributed on a sphere. I'm interested to know what is the distribution of ...
0
votes
2answers
81 views

Addition of probabilities and gambler's fallacy

Say you have a 1 in 6 chance of winning a card game. The more times you play, the higher the odds of you winning. $$P(\text{win over 1 trial}) = 1/6 \\ P(\text{win over 2 trials}) = 1/6 + 1/6 \\ ... ...
2
votes
0answers
65 views

How to construct a uniform joint distribution

I have a question that is critical to my work, but I am not sure if it is any possible. Assume that you have two uniform random variables X and Y. The product distribution of Z=XY is not a uniform. ...
2
votes
0answers
136 views

Finding functions where the increase over a random interval is Poisson distributed

I'm trying to construct a type of function $f(t_1, t_2)$ that counts the number of deterministically simulated Poisson events between two points in time. We can use a single valued function ...
1
vote
1answer
268 views

problem on random variable in probability

A game consists of first rolling an ordinary 6-sided die once and then tossing a fair coin once. The score, which consist of adding the number of spots showing on the die to the number of heads ...
2
votes
3answers
394 views

Random number generator with discrete probability distribution

Is there a general algorithm for implementing a PRNG with a probability distribution?
2
votes
1answer
202 views

Average number of bins occupied when throwing $n$ balls into $N$ bins

There are $n$ balls and $N$ bins. At each time, a ball is thrown in one bin of $N$ bins at random. This repeats n times. So that in total $n$ balls are thrown into bins. The question is, on average, ...
0
votes
1answer
85 views

Chernoff type Sum of independent random variables having exponential tails

Say I have n independent variables $\{X_1,X_2 \dots X_n\}$ with Expectation 0 such that $Pr(|X_n| > \alpha) < e^{-\lambda \alpha}$. Can we produce chernoff type inequalities for the sum of these ...
0
votes
0answers
47 views

Property of a random distribution.

I have to get an integral in a previous post Help on an integral.. Some guru gave me hints of how to approximate its value, but I need approximation with largely varying $a$ and $b$. I realized that ...
2
votes
1answer
176 views

Fast generation of Pareto-distributed randoms.

I'm developing a library of routines for generating random numbers for simulations (it's on GitHub). I've included fast routines for normally distributed and exponentially distributed randoms, using ...
2
votes
0answers
253 views

Probability distribution of the product of two independent complex gaussian random variables

I have to calculate the pdf of $Z = X*Y$, where $X \in \mathcal{C}(\mu_x,\Sigma_x)$ and $Y \in \mathcal{C}(\mu_y,\Sigma_y)$, where $\mathcal{C}$ is a complex distribution. It can be assumed that ...
0
votes
1answer
111 views

Probability density function for the normalised sum of N random variables

I was wondering what the PDF looks like for Z= (1/N)*SUM(z_1+...+ z_n), where each z_i is computationally represented by RAND(). What is the behaviour of the PDF as N -> infinity?
2
votes
2answers
116 views

Generating a random number from a given distribution

I have a problem (a part of a Monte Carlo simulation) where I'm given the energy of an incoming particle, $\varepsilon$ and want to split this energy in two parts, randomly generating the fraction ...
1
vote
1answer
114 views

What is the distribution of $\min(r_1, r_2)$?

If I have 2 uniform random numbers $r_1$ and $r_2$ in $[0,1)$, what is the distribution of $\min(r_1, r_2)$? I have a problem I'm trying to get my arms around, and getting some context on this ...
1
vote
1answer
379 views

Generating random numbers with skewed distribution

I want to generate random numbers with skewed distribution. But I have only following information about distribution from the paper : skewed distribution where the value is 1 with probability 0.9 ...
1
vote
1answer
147 views

Random sampling from a conditional bivariate normal distribution

How does one draw a random sample $\begin{bmatrix} X_i \\ Y_i\end{bmatrix}$, $i=1,\ldots,n$ from the conditional distribution of a bivariate normal distribution, given specified values of the the ...
1
vote
0answers
85 views

What discrete distribution is completely determined by its mode and variance, is easy to sample, and has nice border properties?

I need to generate random ordered unranked trees that will be used to test some computer program. I'd like to incorporate some kind of control into the generation process, so that the generated trees ...
8
votes
1answer
277 views

Repeatedly Toss Balls into Bins

$n$ balls are randomly tossed into $m$ bins, each bin can hold $k$ balls. If a ball is tossed into a full bin (already has $k$ balls in it), it can be tossed repeatedly and randomly into the $m$ bins ...
1
vote
1answer
66 views

Finding a distribution for random number generation

I am writing a program for solving the shortest path in travelling salesman problem, with a twist that there are multiple salesmen who partition the cities among themselves, thus creating two part ...
0
votes
1answer
206 views

How to deal with non random data in statistical analysis?

I have a set of monthly water quality data, and I want to use them in a few statistical analysis (such as finding distribution or using in copula models) which require random variables as input. I ...
0
votes
1answer
978 views

Cumulative distribution function determine the random variable

I don't know that determine is the right word, but I try to explain. What I need to understand. :) So.. We know's that if a function fit this conditions: Monotonically non-decreasing for each of its ...
1
vote
1answer
35 views

Off-lattice Brownian bridges in R^3

Start at a point $(0,0,z_0)$ and take $n$ steps of unit length in a random direction (for each step) in $\mathbb{R}^3$. Let such a walk be valid if the position of the last step, and only the last ...
4
votes
3answers
2k views

Repeating something with (1/n)th chance of success n times

Is there anything that can be said about how many attempts it will take to correctly guess a random number out of 1000 numbers? If the number wouldn't change the probability would just increase every ...
1
vote
1answer
279 views

CDF of standard normal random variable never actually is 0 or 1, right?

The CDF of a standard normal random variable is never actually 0 or 1, they only approach 0 and 1, correct?
4
votes
2answers
494 views

Trends in the distribution of reordered digits of Pi (OEIS A096566)

First let me try to describe in more details below the approach of "reordering" digits of Pi, which is used in OEIS A096566 https://oeis.org/A096566 and what I have done analyzing it so far. I am ...
1
vote
0answers
66 views

Are my steps to generate random values based on a given dataset correct?

I have a dataset of 100 cases. Each case has a class {I,II,III,IV,V} and a value A and V, each class appears exactly 20 times in the dataset: ...
1
vote
1answer
641 views

A problem on random variable in probability

I am a starter in maths. I am doing pretty good in all other topics except for probability. I don't know why I am always confused in it. My exams are nearby and I still cant solve simple problems. Can ...
0
votes
1answer
124 views

Inner product of two vectors with Rademacher random entries

I am lost with the signs cancellation. Please help me to calculate this inner pruduct. Let $a$ and $b$ be two $2m$ dimentional vectors such that their entries are Rademacher random variables and ...
0
votes
0answers
434 views

Prove that $aX + bY$ is a random variable for all $a, b$ in $\mathbb{R}$

Given $X$ and $Y$ as random variable, how to prove that $aX + bY$ as random variable for all $a, b$ in $\mathbb{R}$? (from Karr) $$ \{X + Y <t\} = \bigcup\limits_{r\in\mathbb Q}\{X < ...
0
votes
1answer
255 views

maximum of two non central chi squared random variable

Let $$s_i \sim \chi(k_i, \lambda_i), i\in \{ 1, 2\}$$ be two non-central chi-squared random variables with $k_i$ degrees of freedom and $\lambda_i$ parameter of non-centrality I am wondering if ...
0
votes
2answers
171 views

Selecting numbers on a number line where distribution tends to cluster at one end.

Lets say I've got a number line from $1$ to $100$. I want to randomly select $20$ integer numbers from the number line. But I want the numbers to tend to come from say $1$-$50$, with only a few coming ...
0
votes
1answer
37 views

what should be the frequency distribution of the eigenvalues of a randomly generated hermitian matrix?

I'm getting the eigenvalues of a randomly generated hermitian matrix distributed like a normal probabilistic distribution(crowded in the middle values ) but my sir told me that it should be a ...
2
votes
0answers
46 views

Generate random numbers that are sums of hidden variables

I have $Y = A X$ where: $Y$ is an $m$ vector of random variables $X$ is an $n$ vector of random variables, uniformly distributed in $[0, 1]$ $m \ll n$, ($n$ ~ $m!$) $A$ is an $m \times n$ $0/1$ ...
0
votes
1answer
109 views

How to generate random samples from a ratio distribution?

I have two i.i.d. random variables $X$ and $Y$ and I want to generate a set of $n$ random samples from the distribution of the ratio between the two variables $Z=X/Y$. The pdf of $Z$ is described by: ...
0
votes
1answer
281 views

Expected value for the number of goals in a game

I'm trying to use odds data from bookmakers to estimate the expected number of goals in a game. We have these known facts: P(o4.5) = 0.573 P(o5.5) = 0.458 P(o6.5) = 0.279 P(o4.5) is the ...
1
vote
1answer
168 views

Help with a short paper - cumulative binomial probability estimates

I was hoping someone could help me with a brief statement I can't understand in a book. The problem I have is with the final line of the following section of Lemma 2.2 (on the second page): Since ...