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Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.Two events are independent, statistically independent, or stochastically independent [1] if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds.
It is the opposite of determinism and related to chance. It is highly relevant to the philosophical problem of free will, particularly in the form of metaphysical libertarianism. In science, most specifically quantum theory in physics, indeterminism is the belief that no event is certain and the entire outcome of anything is probabilistic.
Therefore, it is not opposite day, but if you say it is a normal day it would be considered a normal day, which contradicts the fact that it has previously been stated that it is an opposite day. Richard's paradox : We appear to be able to use simple English to define a decimal expansion in a way that is self-contradictory.
[2] [3] A more extreme antonym of determinism is indeterminism, or the view that events are not deterministically caused but rather occur due to random chance. Historically, debates about determinism have involved many philosophical positions and given rise to multiple varieties or interpretations of determinism.
In logic, two propositions and are mutually exclusive if it is not logically possible for them to be true at the same time; that is, () is a tautology. To say that more than two propositions are mutually exclusive, depending on the context, means either 1. "() () is a tautology" (it is not logically possible for more than one proposition to be true) or 2. "() is a tautology" (it is not ...
More precisely, a real-valued continuous-time stochastic process with a probability space (,,) is separable if its index set has a dense countable subset and there is a set of probability zero, so () =, such that for every open set and every closed set = (,), the two events {} and {} differ from each other at most on a subset of .
Nowadays it feels like few things on the internet could surprise its users. Yet many images on social media make them raise an eyebrow, nevertheless, often thanks to (unsuccessful) editing. From ...
Students of statistics and probability theory sometimes develop misconceptions about the normal distribution, ideas that may seem plausible but are mathematically untrue. For example, it is sometimes mistakenly thought that two linearly uncorrelated, normally distributed random variables must be statistically independent.