Search results
Results From The WOW.Com Content Network
Independent, in Independence (probability theory), a variable whose occurrence does not affect the probability of occurrence of another; Independence (mathematical logic), unprovability of a sentence (e.g. the Parallel postulate) from other sentences (e.g. the remaining Euclidean geometry axioms)
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.
Independence is a condition of a nation, country, or state, in which residents and population, or some portion thereof, exercise self-government, and usually sovereignty, over its territory. The opposite of independence is the status of a dependent territory or colony.
There are cases in which uncorrelatedness does imply independence. One of these cases is the one in which both random variables are two-valued (so each can be linearly transformed to have a Bernoulli distribution). [3]
A chart showing a uniform distribution. In probability theory and statistics, a collection of random variables is independent and identically distributed (i.i.d., iid, or IID) if each random variable has the same probability distribution as the others and all are mutually independent. [1]
In mathematical logic, independence is the unprovability of some specific sentence from some specific set of other sentences. The sentences in this set are referred to as "axioms". The sentences in this set are referred to as "axioms".
Stochastic independence implies mean independence, but the converse is not true.; [1] [2] moreover, mean independence implies uncorrelatedness while the converse is not true. Unlike stochastic independence and uncorrelatedness, mean independence is not symmetric: it is possible for Y {\displaystyle Y} to be mean-independent of X {\displaystyle ...
In mathematics, a function is a rule for taking an input (in the simplest case, a number or set of numbers) [5] and providing an output (which may also be a number). [5] A symbol that stands for an arbitrary input is called an independent variable, while a symbol that stands for an arbitrary output is called a dependent variable. [6]