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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.
Primary, alternate, contingency and emergency (PACE) is a methodology used to build a communication plan. [1] The method requires the author to determine the different stakeholders or parties that need to communicate and then determine, if possible, the best four, different, redundant forms of communication between each of those parties.
Causal inference is the process of determining the independent, actual effect of a particular phenomenon that is a component of a larger system. The main difference between causal inference and inference of association is that causal inference analyzes the response of an effect variable when a cause of the effect variable is changed.
In semiotics, linguistics, sociology and anthropology, context refers to those objects or entities which surround a focal event, in these disciplines typically a communicative event, of some kind. Context is "a frame that surrounds the event and provides resources for its appropriate interpretation".
(That is, the two dice are independent.) If, however, the 1st die's result is a 3, and someone tells you about a third event - that the sum of the two results is even - then this extra unit of information restricts the options for the 2nd result to an odd number. In other words, two events can be independent, but NOT conditionally independent. [2]
I(p 1 ·p 2) = I(p 1) + I(p 2): the information learned from independent events is the sum of the information learned from each event. Given two independent events, if the first event can yield one of n equiprobable outcomes and another has one of m equiprobable outcomes then there are mn equiprobable outcomes of the joint event. This means ...
An event with probability 100% is perfectly unsurprising and yields no information. The less probable an event is, the more surprising it is and the more information it yields. If two independent events are measured separately, the total amount of information is the sum of the self-informations of the individual events.
It is possible to have multiple independent variables or multiple dependent variables. For instance, in multivariable calculus, one often encounters functions of the form z = f(x,y), where z is a dependent variable and x and y are independent variables. [8] Functions with multiple outputs are often referred to as vector-valued functions.