![]() ![]() Rare events are said to fall along the "long tail" of the distribution.īack to pseudorandomness. ![]() In the normal distribution, you are more likely to be clustered around the mean (0 in the above example), but still have rare instances of finding oneself 2 or even 3 standard deviations from the mean.įor reference: about two-thirds of cases fall within 1 standard deviation from the mean (that is, +/- 1) 95% are within 2 s.d. In the case of the uniform, which is flat everywhere, you have no difference between x-axis locations. That is, the likelihood of something is governed by the height of the pdf curve at some location on the x-axis. Note a few things here: the probability of any one event is given by evaluating the pdf (probability density function) at an x-location. It looks like a logistic function (one asymptote to the left at y=0, then function slopes up to another asymptote at y=1 to the right. This is also just called the cumulative distribution function (cdf) of the normal. This means things cluster around 0, the center, with some spread (=variation, whose square root is standard deviation sigma).įun fact: if you take the integral of this function, it converges but cannot be expressed with any mathematical instruments we already have, so a name was invented for it: erf(x). (More Technical) if you draw from a bell curve pdf(x) = 1/(sigma*sqrt) * e^ then your numbers are said to be normally distributed, with mean 0 and standard deviation sigma. ![]() if you are drawing numbers from a distribution that is flat, such as pdf(x) = c over some interval : This is called the uniform distribution, and every event is equally likely. The computer proceeds to draw pseudorandom numbers according to some distribution of what is called a "random variable", like the analogy of a function but to probability spaces. This is an example of something which can, by definition does, transcend human understanding. Something can only be considered random relative to your methods of measuring "randomness", that is, the entropy of the medium. ![]() The computer uses pseudorandom numbers to effectively model "randomness", which is really only a theoretical concept. What it is doing is coldly calculating probabilities using formulas, and simply not messing up because it has been pre-programmed. Whether or not the computer is random is not the point. ![]()
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