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In probability theory, conditional dependence is a relationship between two or more events that are dependent when a third event occurs. [1] [2] For example, if and are two events that individually increase the probability of a third event , and do not directly affect each other, then initially (when it has not been observed whether or not the ...
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]
An event, however, is any subset of the sample space, including any singleton set (an elementary event), the empty set (an impossible event, with probability zero) and the sample space itself (a certain event, with probability one). Other events are proper subsets of the sample space that contain multiple elements. So, for example, potential ...
event A subset of the sample space of a procedure or experiment (i.e. a possible outcome) to which a probability can be assigned. For example, on rolling a die, "getting a three" is an event (with a probability of 1 ⁄ 6 if the die is fair), as is "getting a five or a six" (with a probability of 1 ⁄ 3).
In probability, weak dependence of random variables is a generalization of independence that is weaker than the concept of a martingale [citation needed].A (time) sequence of random variables is weakly dependent if distinct portions of the sequence have a covariance that asymptotically decreases to 0 as the blocks are further separated in time.
Any combination of events using the operations and, or, and not is also an event, and assigning probabilities to all outcomes generates a probability for every event. In technical terms, this means that the set of events and the three operations together constitute a Boolean algebra of sets, with an associated probability function .
Donald Trump said he'd launch the “largest deportation” in American history. To do it, he'll need to address a massive backlog in immigration court cases.
In probability theory, conditional independence describes situations wherein an observation is irrelevant or redundant when evaluating the certainty of a hypothesis. . Conditional independence is usually formulated in terms of conditional probability, as a special case where the probability of the hypothesis given the uninformative observation is equal to the probability
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