# Random dating roulette

Using the CLT to approximate normality is certainly a method I would ever advise as (1) you still need other variates to feed the average, so may as well use uniforms in the Box-Müller algorithm, and (2) the accuracy grows quite slowly with the number of simulations.Especially if using a discrete random variable like the result of a dice, even with more than six faces. (2007), a survey on the pros and cons of Gaussian random generators: and looked at the normal fit [or lack thereof] of this sample: First, the fit is not great, especially in the tails, and second, rather obviously, the picture confirms that the number of values taken by the sample is embarrassingly finite. If "manually" includes "mechanical" then you have many options available to you.

Buffon's needle can, therefore, be used to simulate a random variable $X \sim \text(\frac)$ or $X \sim \text(n,\frac)$, and we can adjust the probability of success by altering the lengths of our needles or (perhaps more conveniently) the distance at which we rule the lines.

It seems there is no such thing as a "weighted coin" but if we wish to vary the probability parameter of our Bernoulli or binomial variable to values other than $p = 0.5$, the needle of Georges-Louis Leclerc, Comte de Buffon will allow us to do so.

To simulate the discrete uniform distribution on $$ we roll a six-sided die.

For instance, on my Linux OS, I can check enough, there exists a variant to Box-Müller that avoids using those transcendental functions (see Exercise 2.9 in our book Monte Carlo Statistical Methods): Now, one can argue against this version because of the Exponential variates.

But there also exists a very clever way of simulating those variates If you do not have access to this clock, you can replace this uniform generator by a mechanistic uniform generator, like throwing a dart on a surface with a large number of unit squares $(0,1)^2$ or rolling a ball on a unit interval $(0,1)$ with enough bounces [as in Thomas Bayes' conceptual billiard experiment] or yet throwing matches on a wooden floor with unit width planks and counting the distance to the nearest leftmost separation [as in Buffon's experiment] or yet further to start a roulette wheel with number 1 the lowest and turn the resulting angle of 1 with its starting orientation into a uniform $(0,2\pi)$ draw.