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{{a| | {{a|systems|}}{{d|Stochastic|/stəˈkæstɪk/|adj|}} | ||
Of an event, to have a | Of an independent event, to be random: to have a calculable [[probability]] of occurring that is less than one and greater than zero. To be predictable by reference to probability only. | ||
To qualify as a random distribution, events must be independent, each value must have a non-negative value, and the value of all events must add to 1. There must be a finite possible number of events. | |||
The price of a stock market index at | Compare with [[deterministic]] (describing an event that is precisely predictable, such that it has a probability of 1) and [[uncertain]] (describing an event which is not independent or where controlling conditions are incomplete or unknown such that you cannot assign a probability at all. | ||
===Examples=== | |||
Tossing a coin or rolling dice is stochastic: there are discrete outcomes, each of them is equally likely, but it is impossible to know which will come up in a given instance. Nonetheless, you know the probability of a given outcome exactly. | |||
The next word uttered by a conscious human is neither deterministic not stochastic. It is not governed by, or explainable in terms of, probabilities. | |||
The price of a stock market index at a point in the future ''seems'' stochastic, in that it must be a number and that number must be between zero and the total value of all issued currency in the world, but it isn’t. You can’t assign [[probabilities]] to dependent events controlled by human agency, as [[Standard deviation|David “25-Sigma-Several Days-In-A-Row” Viniar]] would — probably? — tell you. So it really isn’t stochastic. | |||
What Elon Musk is going to say on [[Twitter]] tomorrow is ''uncertain''. There is no way of predicting it, or even assigning a probability to it. It is ''not even random''. | |||
{{sa}} | |||
*[[Uncertain]] | |||
*[[Deterministic]] | |||
*[[Systems theory]] |