Questions relating to (pseudo)randomness, random oracles, and stochastic processes.

learn more… | top users | synonyms

0
votes
0answers
21 views

Randomness of a Sample

While studying about Sampling I went through a question in Data Collection. QUESTION Suppose your population is numbered 000 to 299. Use the random digit sheet by taking consecutive three digits. ...
1
vote
2answers
89 views

Picking 3 random books probability problem

So the question is: Suppose a bookcase holds 6 chemistry, 5 math, 3 physics, and 8 computer science texts. if 3 books are selected, find the probability that none of the math texts are selected. My ...
1
vote
1answer
37 views

Iterated uniform random variables

Define a sequence of r.v.'s {$X_n$}$_{n\ge 1}$ iteratively, such that $X_1\sim\text{Unif}(0,1]$ and $X_{n+1}\sim\text{Unif}(0,X_n]$. Could someone please explain why this is equivalent to: Let a ...
3
votes
3answers
123 views

What is the probability of getting the exact number of expected digits ($0-9$) in $10^6$ digits of $\pi$?

I noticed that at $1$ million digits of $\pi$, none of the digits has the "perfect" expected $100{,}000$ occurrences. My question is what is the probability (if the digits are truly random) of at ...
1
vote
1answer
70 views

Random number generation in MATLAB with condition

How can I generate random numbers in MATLAB with the condition that each new number has a minimum difference with all previously generated numbers for that matrix. So, X = rand(1,20) would generate 20 ...
1
vote
1answer
47 views

Flipping coin(s) to decide who pays the bill

I'm not from a mathematical background. I found this video on YouTube rather confusing. I know basics of probability from school. My question: If a single coin is flipped among 3 people say A, B and C ...
0
votes
1answer
56 views

Probability of coin flip betting

Imagine a situation where you and a friend both have 5 dollars, and you play him in a 50/50 coin flip "duel" where if it flips heads you receive a dollar from them otherwise you lose a dollar to the ...
0
votes
1answer
36 views

Binomial cumulative probability

Here is the question I need help on : Let $X$ be a binomial random variable with p = 0.5 and n = 100. Give $P(X \geq 60)$ rounded to two decimal places without using a calculator (by using ...
4
votes
3answers
211 views

What is in clear mathematical terms the definition for a sequence of integers, to be called *random*?

Sequences of integers might be ordered, totally ordered,... For all such attributes we find definitions in clear mathematical terms. (1) But what is in clear mathematical terms the established and ...
0
votes
0answers
24 views

Sampling from a random distribution with a margin of error

A survey of a population is taken using sampling. It is determined that 70% prefer option A and 30% prefer option B with a margin of error being 5%. Typically when simulating the process with the ...
2
votes
2answers
171 views

What is the mathematical notation for a random number in a certain range?

In school, I was taught to denote a random variable like so: $$R=\{_{0}^{1}$$ This only goes for a random choice between two integers, like a coin flip. How do I write a variable that is equal to a ...
2
votes
2answers
68 views

Is there some predictability in (pseudo-)randomness?

I was wondering if random numbers actually do have some predictability. For example, the digits of $ \pi$ are supposedly random. However, the frequency of some digits "lags" that of other digits. ...
0
votes
1answer
104 views

$\pi$ normal to the base $10$ [closed]

If $\pi$ is normal to base $10$, why would we expect to find a string of ten $0$'s in its decimal expansion?
2
votes
1answer
31 views

Can a collection of random processes be not random?

A friend and I were having a debate about randomness and at one point, I said that it was possible to have a collection of random processes which were not random when "put together." He disagreed. ...
1
vote
2answers
143 views

generate random number from exponential distribution with random right truncation

I need to draw a random number from an exponential distribution (rate $mu$) that is right-truncated with the truncation value coming from a gamma distribution (shape $k$, rate $lambda$). My naive ...
2
votes
1answer
71 views

Good ways to sample $n$ identical and dependent random variables

I'm wondering if there's a good way to talk about sampling identical but dependent random variables where it's also easy to see how the distribution evolves as we move from $n$ random variables to ...
0
votes
0answers
28 views

Probabilistic Method in language membership decision

$F(x,r)$ is a random algorithm to decide membership of input $x \in \{0,1\}^n$ to a language $L$. $r \in \{0,1\}^n$ is randomly selected bits. We know the if indeed $x \in L$, then the probability ...
0
votes
1answer
52 views

Expected value of a sum of random events

Suppose there's a market that has decided to award its most loyal customers. The market sells a certain type of breakfast cereals with a single token in each box. There are n different types of ...
2
votes
1answer
20 views

Can I use one float random number to generate two random numbers, one discrete, one continuous?

I need two random numbers. The first one, u, is discrete and takes 70% of the time the value 0 and 30% of the time the value 1. The second one, v, is continuous and takes values uniformly inside [0, ...
0
votes
0answers
15 views

Will XORing any data with random data produce a random result?

Provided you have a stream of input data and a stream of random data both in the set (0,1). The random is data truly random, that is, unpredictable by the user and ...
0
votes
3answers
103 views

Generate random number with specific probability distribution

Well consider I have a uniform random number generator. How would I craft a function which takes as parameter this RNG, such that the distribution is following a given function? Or more to the point: ...
3
votes
2answers
140 views

Probability a product of $n$ randomly chosen numbers from 1-9 is divisible by 10.

I'm working on a problem where each number is chosen randomly from 1-9. Given $n$ numbers chosen in this manner, we multiply all of these together. I'm looking for the probability that this product is ...
0
votes
0answers
33 views

Divergence of series

Given that a is a non 0 real number and ck is a series of real number for all k natural number where $\sum_{k= 1}^{\infty} c_k^2 = \infty $. If $c_k \to 0$, proof that $lim _{n \to ...
3
votes
1answer
29 views

Distribution of numbers $n = \max(x, y)$ where $x, y$ are random numbers between $0$ and $1$

I define a function $$f = \max(\mbox{rand}(0, 1), \mbox{rand}(0, 1))$$ such that $f$ returns the maximum (greater number) of two random selected numbers between $0$ and $1$. Plotting a histogram for ...
1
vote
2answers
54 views

Variance of sample mean (problems with proof)

Assuming that I have $\{x_1,\ldots, x_N\}$ - an iid (independent identically distributed) sample size $N$ of observations of random variable $\xi$ with unknown mean $m_1$, variance (second central ...
0
votes
0answers
20 views

How do you count a grouping without a sequential count?

So, rather than explaining how this problem pertains to the actual situation I think its easier and a great deal less work to give you a situation that you can visualize. Imagine a person who has ...
2
votes
1answer
63 views

Analogous of Markov's inequality for the lower bound

Consider a positive random variable $X$ and call $E[X]$ its expectation. For any positive $a \in \mathbb{R}$, an upper bound for the probability of $P(X>a)$ is provided by the Markov's Inequality, ...
1
vote
1answer
26 views

Random conversions

I came across a question in StackOverflow which states the following, all is based on natural numbers: Given the function rand5 (which produces random natural numbers 0-4), use it to generate a rand7 ...
2
votes
0answers
36 views

How do you calculate randomness?

Suppose I receive a list of 1 million coinflips, and I want to know how likely it is that the list was randomly generated. My first thought would be to count the number of heads and tails, which ...
0
votes
1answer
29 views

Is there a name for the following random process?

I have a random process which seems to oscillate between extremes in terms of trending but which is locally like a Brownian motion or a fractional Brownian motion. Is there a name for such a ...
0
votes
1answer
24 views

What is the meaning $P[\frac{1}{n}\sum_{k=1}^{n}Z_k \le \frac{1}{2}\text{ for infinitely many }n]=0$

Let $Z_1, Z_2,\ldots$ be independent identically distributed (i.i.d) binary variables with $P[Z_i = 1] = 1-\alpha $ for some $\alpha > \frac{1}{2}$. Using the transformation $X_i=2Z_i-1$ together ...
2
votes
1answer
94 views

Generating a random combination in O(k)?

I need to generate a "fair" random combination of $k$ items chosen from $n$ choices. All the algorithms I've been able to find so far (reservoir sampling, Fisher-Yates shuffle, ...) are of $O(n)$ ...
0
votes
2answers
37 views

Inequality on probability of the sum of random variables

For Independent random variables $X_{i}$ can we write down the following inequality? $$\Pr \left\{ {{X_1} + {X_2} + ... + {X_n} \le k} \right\} \le \Pr \left\{ {{X_1} \le k} \right\}\Pr \left\{ {{X_2} ...
0
votes
1answer
39 views

Random process of the form $X(t)=A^t$ where $A$ is a given random variable

We’re going to look at a random process, which is a sequence of random process, which is a sequence of random variables that depend on time. Let $X(t)=A^t$ where $A$ has the density $f_A (a)=(3/8) ...
3
votes
1answer
40 views

Probability of random assignment to form pairs

So the question goes: I have 100 individuals and 100 different buses, and I randomly assigned each individual to sit on a bus (each bus has equal probability of being selected). How many buses are ...
0
votes
0answers
62 views

random number generation from joint distribution where marginal are independents and known

Let $f(x,y)$ be the joint distribution of $X$ and $Y$, where $X$ and $Y$ are both positive and continuous. I can decompose the joint distribution as $f(x,y)=f(x|y) \, f(y)$ and I can easily generate ...
6
votes
0answers
565 views

Random 3D points uniformly distributed on an ellipse shaped window of a sphere

How can I generate random points uniformly distributed on the surface of a sphere such that a line that originates at the center of the sphere, and passes through one of the points, will intersect a ...
1
vote
2answers
68 views

Sum of Binomial Coefficient products

I am trying to prove that $$\sum\limits_{y=0}^d \frac{{2x \choose y} {2d-2x \choose d-y} }{2d \choose d} = x $$ So far, I have tried using induction on $d$ but I am having trouble using the ...
-1
votes
1answer
66 views

How can I use a Gamma Random Variable to Aproach the Expected value of a exponential random variable function?

I´m working on trying to approach the value of $E\left[ \dfrac{e^x}{x+1} \right]$. Where $x$ is an exponential random variable. All that data I have to work with is a gamma random variable with ...
0
votes
2answers
96 views

Solved - Use Random Number to Derive # based on Probability Table

Update I was able to derive the algorithm and implement it into excel. Thanks for the formula. Something like: ((z-xlbound)/d(x)*d(y))+ylbound See original sheet at end of post Original Post ...
3
votes
2answers
56 views

How to check if a sequence is random?

When I was thinking about various types of pseudo-randomness, the following question struck me: Suppose that a sequence $a_n \in \{0,1\}$ is given. Is there a way to check if it is genuinely ...
2
votes
0answers
78 views

Are humans capable of thinking of a series of random numbers? [closed]

I read in a book today ( the computer music tutorial by curtis roads), that humans are not capable of imagining any long series of truly random numbers. Apparently, the only way to generate a series ...
2
votes
0answers
23 views

What is the test of for randomness

How do you tell if a large sequential sample taken from a 0-1 rectangular parent - and presented as random - is truly random?
1
vote
1answer
47 views

Selecting a random orthogonal polygon

For a certain demo application, I want to create at random a rectilinear polygon with a given number of corners. Selecting random $x$ and $y$ coordinates of each corner is not a good method, since ...
1
vote
2answers
107 views

Expected Value of Identically distributed random variables

I have a very quick question regarding the expected value of two random variables $X,Y$ that are identically distributed and not necessarly independent. Is this equation valid? $E[XY]=E[X^2]$ If ...
0
votes
0answers
41 views

The probability that uniformly distributed integers sum to a given integer

A recent CTF had a problem involving the summation of randomly distributed integers. Specifically: Consider a set $\{X_m\}$ of $M$ integers uniformly selected (with replacement) from the set of ...
1
vote
2answers
26 views

Random number distribution from a different distribution

Suppose I have a random number generator that generates random numbers $x$ with a normal distribution $p(x) \propto e^{-x^2}$ (modulo normalization, but lets keep it simple). Now, out of these ...
0
votes
0answers
15 views

Is it possible to use multiple time scale algorithm here?

Suppose a random sequence is being generated (the next term generated depends on the previous term, but we don't know any distribution) until we hit some specific number. We want to calculate the ...
0
votes
1answer
22 views

Generate random results in a continuous field

How can we generate random results for a field like economical predictions where there is no limited number of results (contrary to a coin with 2 results) and also contrary to a random walk with steps ...
0
votes
1answer
300 views

How Many Unique Character String Can Be Made From 62 Characters?

I'm working on a programming algorithm and need a little math help. I'm in 10th grade and I think the question I'm asking is actually a permutation and combination logic question. Okay, so I've 62 ...