# Tagged Questions

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### probability: arithmetic with random variables.

I have a question of using arithmetic on random variables. Please refer to the following question, to which I will present my solution using the arithmetic (which I thought it's correct but actually ...
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### {Probability}: choosing keys from a pool without replacement

The OP is trying to understand the following question. The OP understand that if you can always write out the term $$P(X=k) \implies (1-\frac{1}{N})(1-\frac{1}{N-1})\cdots(1-\frac{1}{N-k+1}),$$ ...
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### Probability: deviation from the mean

I am having trouble to understand the following. If $S_n=X_1+X_2+......+X_n$, where X_1,X_2 are Bernouli (p). I don't understand this. So you get an intermediate point Constant* sqrt(n). To the ...
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### Random sample and probability

A random sample of 325 new toothbrushes showed that 14 were defective. What is the estimate of the probability that a new toothbrush is not defective? Either a toothbrush is defective or not. What is ...
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### Is an SD card a fair coin… to me?

This morning, I wanted to flip a coin to make a decision but no coins were in reach. There was however an SD card on my desk: Given that I don't know the bias of this SD card, would flipping it be ...
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### Probability in a weighted Random

This is actually a question that came up whilst programming, but i figured this is more a question for the mathematicans: in a database have a set of roughly 500 entries. now i want to get 10 random ...
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### 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 ...
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### Density on the square, expected value

Let $f: [0,1]^2 \rightarrow \Bbb R^{+}$ a density function on the square. I suppose that the random variable $X=(X_1,X_2)$ has the density f with respect to the lebesgue measure. I denote ...
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### 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 ...
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### Asymptotics of sum of binomial distributions

Definition 1: For any random variable $X$, we define $Bin(p,X)$ as a variable with binomial distribution having parameters $p$ and $X$. Definition 2: For all $i \in \mathbb{N}$, define recursively ...
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### 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 ...
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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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### Probability of occurrence after Latin Hypercube sampling and then random sampling

I am using Latin Hypercube sampling to obtain numbers from a Normally Distributed set of data, so that I get a uniform spread of numbers across the Normal Distribution. I then select a number at ...
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### Probability of random variable in Normal Distribution

I've been talking to my lecturer about choosing random values from a Normal Distribution and he says the following: "Roughly 68% of expected values $\in (\mu-\sigma,\mu + \sigma)$ does not imply ...
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### Probability question (grid)

Say I have a grid of 10x7. Every square of that grid is empty. Then, 20 squares, chosen at random, are filled (a square can only be filled once, so no duplicates allowed). What is the probability of ...
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### Probability of collecting all 5 different items at random with different weights

There are 5 different items in a set, each with a weighted chance of being rolled randomly [A-E]. The weights add up to 100%. $$A=5\%, B=10\%, C=15\%, D=30\%, E=40\%$$ You get 1 item every roll no ...
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### 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 ...
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### the maximum of two random variable

The maximum of two random varibles $X$ and $Y$ is: $$Z=\max\{X,Y\}= \begin{cases} X & \text{if } X \geq Y \\ Y & \text{if } Y \geq X \end{cases}$$ I don't understand. So if I roll two dice, ...
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### 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 ...
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### Distribute a population size based on fractions using random number generator drand48()

I have a population size of say 5000 people. Every person belongs to either A, B, C or D category. I want to split the population as per a given fraction provided by user. for example, 99% of A, 0.4% ...
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### Looking for a random statistical biaised function

A common random function is designed like a dice, if you call it many times it will yield approximately the same number of times 1, 2, 3, 4, 5 and 6. Statistically, you could say it's equally spread ...
Let $x_1$ and $x_2$ are independent random variable with p.d.f $f(x_1)$ and $f(x_2)$. How to derive c.d.f and p.d.f of random variable $y$, which $y = \frac{x_1 x_2}{ax_1 x_2 + bx_1 + cx_2 + d}$ ...