# Questions tagged [randomness]

Randomness is the lack of pattern or predictability in events. Randomness is often modeled with probability distributions, but can also be generated by deterministic processes.

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### Is tossing a coin a fair way of randomising a group into two groups?

So myself and my uncle are having an argument over whether a coin flip is truly random. I argue it isn't because in real terms a coin tosser will always manipulate a coin so the result isnt 50/50 ...
8k views

### Generating random numbers manually

How can I manually generate a random number from a given distribution, as for instance, 10 realisations from the standard normal distribution?
5k views

### What is the probability of n people from a list of m people being in a random selection of x people from a list of y people?

If I am selecting 232 people from a pool of 363 people without replacement what is the probability of 2 of a list of 12 specific people being in that selection? This is a random draw for an ultra ...
8k views

### Can someone help to explain the difference between independent and random?

In statistics, does independent and random describe the same characteristics? What's the difference between them? We often come across the description like "two independent random variables" or "...
23k views

### Can non-random samples be analyzed using standard statistical tests?

Many clinical studies are based on non-random samples. However, most standard tests (e.g. t-tests, ANOVA, linear regression, logistic regression) are based on the assumption that samples contain "...
5k views

### What is wrong with this “naive” shuffling algorithm?

This is a follow-up to a Stackoverflow question about shuffling an array randomly. There are established algorithms (such as the Knuth-Fisher-Yates Shuffle) that one should use to shuffle an array, ...
630 views

### High autocorrelation when taking the L-th order of difference of a sequence of independent random numbers

To explain this question in more detail, I'll first elaborate my approach: I simulated a sequence of independent random numbers $X = \{x_1,...,x_N\}$. I then take $L$ times the difference; i.e. I ...
797 views

28 views

### How best to form many short, independent random numbers from one long random number?

I have 20 digit, uniformly distributed random numbers, downloaded from random.org (because the numbers from that source are based on variations in atmospheric pressure rather than a mathematical ...
933 views

### Geometric Brownian motion without drift

Let's say we have geometric Brownian motion: $$dS_t = \mu S_tdt + \sigma S_tdW_t$$ Then the SDE becomes: $$S_t = S_0\exp\left(\left(\mu - \frac{\sigma^2}{2}\right)t + \sigma W_t\right)$$ Say $\mu$ ...
389 views

### What is the difference between a Lag plot and a Poincare plot?

So I recently came across Poincaré plots (Wiki) which plots x(t) against x(t+1). Thereafter I found out about lag plots (Description)which seem to do the same thing just the other way around, i.e. x(t)...
112 views

### Occurrence of at least 1 HT and HH in sequences of 4 coin flips not equally likely

I was reading this interesting article on hot hands and streaks in sports. The article revolves around the 16 possible sequences of 4 coin flips (H = heads, T = tails): ...
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### Best process for randomly drawing an odd and an even number

I want to draw a random number from 1 to 100. If this number is even, I want to then draw a random number from the odd numbers between 1 and 100. If the first number is odd, I want to draw a random ...