# Tagged Questions

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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 - ...
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### 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 ...
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### 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. $n = 3$): ...
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### 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 ...
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### 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 ...
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### 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? ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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: ...
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### 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. ...
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### 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?
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### 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 ...
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### 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 ...
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 ...