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An event defines a complementary event, namely the complementary set (the event not occurring), and together these define a Bernoulli trial: did the event occur or not? Typically, when the sample space is finite, any subset of the sample space is an event (that is, all elements of the power set of the sample space are defined as events). [5]
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]
The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur. [note 1] [1] [2] This number is often expressed as a percentage (%), ranging from 0% to 100%. A simple example is the tossing of a fair (unbiased) coin.
Also confidence coefficient. A number indicating the probability that the confidence interval (range) captures the true population mean. For example, a confidence interval with a 95% confidence level has a 95% chance of capturing the population mean. Technically, this means that, if the experiment were repeated many times, 95% of the CIs computed at this level would contain the true population ...
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 .
In this situation, the event A can be analyzed by a conditional probability with respect to B. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P(A|B) [2] or occasionally P B (A).
The event that contains all possible outcomes of an experiment is its sample space. A single outcome can be a part of many different events. [4] Typically, when the sample space is finite, any subset of the sample space is an event (that is, all elements of the power set of the sample space are defined as