Search results
Results from the WOW.Com Content Network
In probability theory, the sample space (also called sample description space, [1] possibility space, [2] or outcome space [3]) of an experiment or random trial is the set of all possible outcomes or results of that experiment. [4]
This is not a one-to-one correspondence between {0,1} ∞ and [0,1] however: it is an isomorphism modulo zero, which allows for treating the two probability spaces as two forms of the same probability space. In fact, all non-pathological non-atomic probability spaces are the same in this sense. They are so-called standard probability spaces ...
In statistics, a sampling distribution or finite-sample distribution is the probability distribution of a given random-sample-based statistic.If an arbitrarily large number of samples, each involving multiple observations (data points), were separately used in order to compute one value of a statistic (such as, for example, the sample mean or sample variance) for each sample, then the sampling ...
A probability distribution is a mathematical description of the probabilities of events, subsets of the sample space. The sample space, often represented in notation by , is the set of all possible outcomes of a random phenomenon being observed. The sample space may be any set: a set of real numbers, a set of descriptive labels, a set of ...
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). However, this approach does not work well in cases where the sample space is uncountably infinite (most notably when the outcome must be some real number).
A random experiment is described or modeled by a mathematical construct known as a probability space. A probability space is constructed and defined with a specific kind of experiment or trial in mind. A mathematical description of an experiment consists of three parts: A sample space, Ω (or S), which is the set of all possible outcomes.
A Bernoulli process is a finite or infinite sequence of independent random variables X 1, X 2, X 3, ..., such that . for each i, the value of X i is either 0 or 1;; for all values of , the probability p that X i = 1 is the same.
Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event.