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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.
The dependent variable is the event expected to change when the independent variable is manipulated. [ 11 ] In data mining tools (for multivariate statistics and machine learning ), the dependent variable is assigned a role as target variable (or in some tools as label attribute ), while an independent variable may be assigned a role as regular ...
In essence probability is influenced by a person's information about the possible occurrence of an event. For example, let the event be 'I have a new phone'; event be 'I have a new watch'; and event be 'I am happy'; and suppose that having either a new phone or a new watch increases the probability of my being happy.
Events A and B can be assumed to be independent i.e. knowledge that A is late has minimal to no change on the probability that B will be late. However, if a third event is introduced, person A and person B live in the same neighborhood, the two events are now considered not conditionally independent.
Independent: Each outcome will not affect the other outcome (for from 1 to 10), which means the variables , …, are independent of each other. Identically distributed : Regardless of whether the coin is fair (with a probability of 1/2 for heads) or biased, as long as the same coin is used for each flip, the probability of getting heads remains ...
In probability theory, a pairwise independent collection of random variables is a set of random variables any two of which are independent. [1] Any collection of mutually independent random variables is pairwise independent, but some pairwise independent collections are not mutually independent.
While the number of independent random events grows, the related joint probability value decreases rapidly to zero, according to a negative exponential law. Similarly, two absolutely continuous random variables are independent if and only if , (,) = ()
Independent events vs. mutually exclusive events The concepts of mutually independent events and mutually exclusive events are separate and distinct. The following table contrasts results for the two cases (provided that the probability of the conditioning event is not zero).