1
vote
2answers
41 views

What is the expected value of this sum (drawing slips from a bag)?

Suppose there are thirteen slips in a bag, labelled 1-13. If I draw a 10, 11, 12, or 13 then I stop adding to the sum and return the sum. If not, I add the number I draw to the current sum and place ...
0
votes
0answers
54 views

Probability Question involving Probability Mass Function/Random Variables

Problem: When a paging system transmits a message, the probability that it will be received correctly by the appropriate pager is p. To ensure that the message is correctly received at least once, the ...
1
vote
2answers
41 views

Median of i.i.d. uniform random variables on the interval $[-1/2, 1/2]$

Let $X_1, X_2, \ldots , X_{999}$ be independent and identically distributed random variables on the interval $[-1/2, 1/2]$. Let $X_{500}$ be the empirical median; that is, $X_{500} = X_k$ for some ...
0
votes
1answer
192 views

Finding the expected value of the length of a minimal spanning tree of n randomly generated nodes bound in a box with edge length a.

Say we specify a number (n) of random points (x,y), bound within the axes and x=a, y=a. Given the number of points and the constraints on the boundaries, how can you calculate the expected value of ...
0
votes
2answers
50 views

Calculating the expected value of n randomly generated numbers?

Say I have a random number generator that will generate x numbers - not necessarily integers - on the continuous range between a and b. How can I calculate the expected values for these numbers? My ...
1
vote
0answers
28 views

Probability of a specified sequence in a random data set

This is a problem which I have encountered while programming, but I imagine this community would be better able to solve it. Suppose we have a number, N, of boxes in a row. In each of these boxes is ...
2
votes
4answers
51 views

The Objectivity of Statistical Testing

I have a very generic question about applied statistics. Suppose, to make things simple, we have a biased coin with probability $p$ of landing heads. We want to determine if our coin is truly fair - ...
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
68 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
53 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 ...
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
29 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 ...
30
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
50 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
96 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
116 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
284 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
39 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
302 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
47 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) ...
12
votes
1answer
276 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
106 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
61 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
269 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
148 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
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
119 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
160 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
215 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
144 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
394 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
44 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
68 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
86 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
252 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
177 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 ...
2
votes
2answers
670 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
310 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
305 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 ...
1
vote
1answer
215 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
501 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
36 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
139 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
388 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
289 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 ...
4
votes
2answers
502 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
400 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
74 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
654 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 ...