Random Number Generation

Why is achieving 'true' randomness on purpose considered practically impossible?

What condition must a uniform distribution satisfy?

A sequence of numbers claims to be statistically random. What key characteristic must it exhibit?

Why might a sequence of numbers that alternates values above and below 0.5 not be considered independent?

What does it mean for a sequence of pseudo-random numbers to be 'repeatable'?

Which function in R is used to generate a series of uniform pseudo-random numbers?

In R, what is the primary purpose of the set.seed() function when generating random numbers?

In the context of the Linear Congruential Method, what does 'mod m' represent?

What is a critical consideration when evaluating the suitability of a Linear Congruential Generator (LCG) for generating random numbers?

How are random numbers between 0 and 1 derived in the Linear Congruential Method, given a sequence of integers X1, X2, ... Xn and a modulus m?

What is a crucial condition that independence imposes on a sequence of random numbers?

Why is the repeatability of pseudo-random numbers considered fundamental in science and programming?

If someone says, 'I'll just say the first number that pops into my head, and that's it, random,' what key aspect of true randomness are they overlooking?

You survey a group of people, asking them to pick a random number from 1 to 10. What outcome is statistically most likely based on the information provided?

True or False: Statistical randomness implies 'true' randomness.

What two important properties are needed in a sequence of random numbers?

If the probability of getting a number between 0.25 and 0.55 extracted from a uniform probability distribution is 0.30, what can we say about extracting a number between 0.30 and 0.60?

With a = 0 and b = 1, calculate the mean from a uniform distribution.

With a = 0 and b = 1, calculate the variation from a uniform distribution.

What values are acceptable in the expression: 0 ≤ x ≤ 1

If a random variable $x$ has a continuous uniform distribution between 0 and 1, what is the probability that $x$ is exactly equal to 0.5?

Which of the following is NOT a typical consideration when generating pseudo-random numbers?

Why is human randomness not truly uniform?

What is a disadvantage of the method shown in the presentation?

Which of the following is not a consideration when looking at deviations from ideal number sequences?

Given a starting point of the algorithm, which characteristic should a strong random number generator have?

Which of these is not a parameter in the formula for the Liner Congruential Method?

The Linear Congruential Method results in a number with cycle 4. What does this tell us about the method?

I run runif(10) in R and get a sequence of numbers. What is the result if instead I run set.seed(2023) then runif(10)?

Which is the purpose of pseudo random numbers

Which parameters are needed in the Liner Congruential Method?

Which one is a feature of the Liner Congruential Method?

Which one is a condition for a good Linear Congruential Method?

Why is computer security mentioned in the introduction?

Which one isn't a possible deviation from the ideal numbers?

What is the main functionality of the runif function in R?

When discussing the properties of random numbers, what does 'uniformity' refer to?

Why is it important to develop methods for generating random numbers when simulating stochastic behavior using computer simulation?

What is 'statistical randomness' in the context of computer-generated random numbers?

In the context of random number sequences, what does the property of 'independence' imply?

How is a continuous uniform distribution typically defined in the context of generating random numbers?

If a sequence of numbers alternates between values above and below the median, what property of statistical randomness might be violated?

Why do computer simulations typically rely on pseudo-random numbers rather than truly random numbers?

What is the primary goal of a deterministic algorithm used to generate pseudo-random numbers?

What is one potential deviation from the ideal properties of random numbers that can occur when using pseudo-random number generators?

What is a key consideration when generating pseudo-random numbers for use in simulations?

Why is the length of the cycle, referring to the number of generated values ​​before repetition, an important consideration when using pseudo-random number generators?

Why is repeatability an important property of pseudo-random number generators?

What does the set.seed() function accomplish in R when generating random numbers?

If you run set.seed(123) followed by runif(5) in R, and then repeat these commands, what will happen?

What is the purpose of the runif() function in R?

If you do not use the set.seed() function before calling runif() in R, what can you expect?

What is the primary function of the Linear Congruential Method?

In the Linear Congruential Method formula $X_i = (aX_{i-1} + c) ext{mod } m$, what does '$m$' represent?

In the Linear Congruential Method, what role does the seed value ($X_0$) play?

What are the conditions for choosing the parameters $m$, $a$, and $c$ in the Linear Congruential Method?

If a Linear Congruential Generator has a short cycle, what is the primary consequence?

After calculating x mod m in R, what operation is then performed to generate a random number (u) between 0 and 1?

What does uniformity ensure in the context of generating random numbers?

If a sequence of numbers is considered 'unrandom', what is a potential observation someone may make?

What is a characteristic of randomness that asking humans to pick numbers lacks?

What is implied by 'Pseudo' when generating numbers?

The text talks about simulating a donut shop, why does it mention it?

According to the slide entitled 'Uniformity', what is observable about a visual distribution of numbers that are generated near zero and one?

I have a list of decimal numbers between 0 and 1, what is the second requirement they must respect?

If the probability of getting a number less or equal to 0.3589 is 0.3589 based on a uniform distribution [0,1], what will the probability be of getting a number less or equal to 0.7?

Running the following code 'set.seed(2023); runif(10)', what will happen if I run it again?

A simulation's results are assessed for validity because of what?

Which of the following is the correct notation for calculating a probability area?

Given a number x = 0.8, what does this tell us about $F(x)$ if $0 \leq x \leq 1$?

I run '1cm(n=8, x0=4, a = 13, c = 0, m = 64)' and get the following output '[1] 0.0625 0.8125 0.5625 0.3125 0.0625 0.8125 0.5625 0.3125', what can I say about that specific choice of parameters?