0
votes
0answers
6 views

Random numbers with groupings

I have 9 items, I need to pick a random item and I would like each item to be just as likely as the others to be chosen. I'm assuming my RNG is perfectly. Currently I am picking a random number ...
1
vote
0answers
23 views

Generate correlated random numbers precisely

Let's assume I want to generate k samples of n random numbers, that are correlated according to a given correlation matrix C (e.g. $n = 3$): ...
0
votes
1answer
33 views

Measuring degrees of randomness

Imagine, for simplicity's sake, that we have a set of numbers, each equal to either 0 or 1. Let's call each a bit. Rationally, if the set is completely random, and reasonably large, the probability ...
0
votes
0answers
24 views

Random sample taken, what is probability?

It was determined that 22% of all stock investors are retired people. In addition, 38% of all U.S. adults invest in mutual funds. Suppose a random sample of 20 stock investors is taken. a. What is ...
1
vote
2answers
19 views

Show that $Cov(X,Y) \geq -23$

if $X,Y$ are two random variables and: $Var(X) = Var( Y) = 23$ how can i show that $Cov(X,Y)\geq -23$ can someone give me some hints on how to show it?(not an answer) i know that $Cov(X,Y) = E(XY) ...
0
votes
0answers
27 views

Spatial randomness of 2-tuples

Lets consider a sequence of 2-tuples $\{(x_i, y_i)\}_{i=1}^n$ in a bounded 2D space. My goal is to investigate the random distribution of these 2-tuples. Can I deduce the spatial randomness of ...
28
votes
3answers
4k views

Why does this not seem to be random?

I was running a procedure to be like one of those games were people try to guess a number between 1 and 100 where there are 100 people guessing.I then averaged how many different guesses there are. ...
2
votes
1answer
49 views

Independent sequences

Let $\{x_i\}_{i = 1, ...,n}$ , $\{y_i\}_{i = 1, ...,n}$ be sequences generated by a pseudo-random number generator using different seed keys, for example $ x_0$ and $y_0$. Are $\{x_i\}$ and $\{y_i\}$ ...
1
vote
1answer
81 views

Searching for random items in a set of lists

This is a programming question, but I'm interested in the math behind it so I think it's better asked here. Say I have a list of items and I'm looking for one item in the list that satisfies a ...
0
votes
3answers
109 views

How to discourage contestants from entering a lottery twice?

Suppose you have a lottery. And you want to prevent participants from buying multiple tickets. What would be the best way to discourage this? For example, increasing the win-chance for all previously ...
1
vote
1answer
200 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 ...
0
votes
1answer
37 views

Project on generating random numbers on GPU

I have been assigned a project on generating random numbers (specifically lognormal random numbers) on gpu. I have knowledge of probability and statistics and some programming experience but I do not ...
1
vote
2answers
286 views

Creating Custom Random Number Generator

My statistics are rusty, but here's what I'm trying to do. Creating an application around football and have this distribution around rushing yards per attempt. ...
0
votes
2answers
43 views

Generating a random number of higher range

I had a discussion with my friend about writing a function (a computer program) which generates 9 values randomly using a random number generator which generates 4 values, i.e I have a PRNG rand(4) ...
0
votes
0answers
90 views

Nontransitive dice

Here is an introduction to nontransitive dice. The question is: given $n$-player with a $m$-sided dice each one, the what is the minimum of $m$ for a fixed $n$ to produce nontransitivity? Here is ...
9
votes
0answers
187 views

Does $\pi$ satisfy the law of the iterated logarithm?

It is widely conjectured that $\pi$ is normal in base $2$. But what about the law of the iterated logarithm? Namely, if $x_n$ is the $n$th binary digit of $\pi$, does it seem likely (from ...
0
votes
1answer
97 views

Probability of Specific event occuring between 2 events?

Forgive me beforehand for what may be a question with an obvious seolution, but I havent had statistics courses in quite some time. I have an Excel File of approximately 3000 Events, each event has a ...
0
votes
1answer
56 views

Expected length of the “greedy” increasing sub-sequence?

Given a sequence of random unique integers of length $n$, if I select every element that is the largest so far how how many elements should I expect to select? This seems superficially similar to ...
2
votes
0answers
218 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
0answers
129 views

Transformation of pdf to calculate cdf

A random variable $X$ has a pdf given by $$\displaystyle f(x) = \frac{2(x+2)}{25}, -2 < x <3$$ Let $Y=X^2$ be a transformation of $X$. $1$. Is this transformation one-to-one? Find the ...
0
votes
1answer
106 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
108 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
126 views

Rademacher random variables in terms of Bernoulli

I've found out that Rademacher random variables and Bernoulli random variables plays an important role in Probability theory. I am wondering how they are connected. For example, Let $r_i, i=1, ...
1
vote
1answer
195 views

Simple random sample without replacement

I have a data file from which I wish to create a uniformly distributed simple random sample, without replacement. Will the following algorithm give me an unbiased result? ...
3
votes
1answer
123 views

Best estimate for random values

Due to work related issues I can't discuss the exact question I want to ask, but I thought of a silly little example that conveys the same idea. Lets say the number of candy that comes in a package ...
1
vote
1answer
327 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 ...
0
votes
1answer
43 views

What are the advanatages of CDFs for RNG over simple random sampling?

If I understand Cumulative Distribution Functions (CDFs) correctly, they can be used for random number generation from a given dataset as follows: Build a CDF that maps data points to an ordinal ...
0
votes
2answers
66 views

Simple probability mass function question

I was wondering why given the probability of an event $P(X>n)=\frac{1}{(n+1)}$ then $P(X=n)=\frac{1}{n(n+1)}$. Could anyone lend me some help please? Thank you so much
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 ...
0
votes
1answer
217 views

Draw Random point Rectangle and Circle.

Plot $15$ points at random (a) inside a rectangle $3$ inches $\times$ $4$ inches. (b) inside a circle of $4$ inches. I think need to use Random Number table. It is a practical problem ...
0
votes
1answer
165 views

Better alternative to run tests for testing randomness

Is there a better alternative to using run tables for testing for randomness in a sample? Currently, for statistical process control charting, I am testing the number of runs identified in a sample ...
1
vote
1answer
526 views

What does relaxing the iid assumptions mean? Intuitive and technical perspectives.

I believe the most restrictive assumption we can place on a series of observations is that they are iid. It is possible to relax these assumptions. For example relaxing the independent distribution ...
2
votes
2answers
270 views

Statistics Probability Help

I just began to take this stats course in HS and I'm a little stuck on these 2 problems below. Can anybody please help me out with the solutions? Thank you. Anything is appreciated. Let $Y$ be a ...
3
votes
2answers
250 views

The probability for guessing a dynamic value (one that changes for each wrong guess)

Please correct me if I am wrong... For a random number X between 1 and 100, the probability for guessing X correctly would be 1/100 For 2 random numbers X and Y between 1 and 100, the probability ...
0
votes
1answer
179 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 ...
2
votes
1answer
410 views

Random Variable Probability Russian Roulette

I am very confused on this one. Any help in how to solve it and what probability rule to use would be appreciated. Consider the situation in which a person played Russian roulette (one bullet, 6 ...
1
vote
0answers
35 views

What is a good way to deal with finite trains from random variables?

EDIT: Disregard this question if it is formulated too confusing. This link provides you with the updated version of the same question What is the most powerful test for process discrimination based ...
1
vote
1answer
133 views

Diehard RNG tests

If my PRNG passes most or all diehard tests does it mean it is secure enough for practical usage? Should I test it with other programms, to ensure it's security? Results of tests: ...
2
votes
1answer
318 views

Are squares of independent random variables independent?

If X and Y are independent random variables both with the same mean (0) and variance, how about $X^2$ and $Y^2$? I tried calculating E($X^2Y^2$)-E($X^2$)E($Y^2$) but haven't been able to get anywhere. ...
1
vote
1answer
258 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?
0
votes
0answers
43 views

Cauchy Random Variable Question [duplicate]

Possible Duplicate: How calculate the probability density function of $Z = X_1/X_2$ Need help with the following problem: Suppose that X and Y are independent normal random variables with ...
3
votes
2answers
414 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 ...
3
votes
1answer
388 views

How do I calculate the probability distribution of the percentage of a binary random variable?

I have an urn containing balls that are all either black or red. I'm interested in discovering the percentage of balls that are red. But I can only sample from the urn (without replacement), so the ...
0
votes
0answers
73 views

Calculating the confidence interval

I've collected data such as mean $ $ and standard deviation $b$ values for several experimental studies, each of which was examined $n$ cases. I would like to report the results with the confidence ...
1
vote
1answer
588 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 ...
2
votes
1answer
78 views

$\chi^2$ test and sampling variance

Let $f(x)$ denote the pdf of a $\chi^2$-distribution with $n\in\mathbb{N}$ degrees of freedom given by $$f(x) = \frac{2^{-n/2}}{\Gamma(n/2)}\cdot x^{n/2-1}\cdot\mathrm ...
2
votes
1answer
156 views

Is the expectation $E[\xi U'(\xi)]$ finite?

I encounter the following problem today. It seems a simple question. Let $U$ be a real function from $R^+\rightarrow \bar{R}$ satisfying the following conditions: (1) $U$ is concave, continuous, ...
0
votes
1answer
97 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
262 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 ...
5
votes
2answers
288 views

Name this paradox about most common first digits in numbers

I remember hearing about a paradox (not a real paradox, more of a surprising oddity) about frequency of the first digit in a random number being most likely 1, second most likely 2, etc. This was for ...