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  2. Markov property - Wikipedia

    en.wikipedia.org/wiki/Markov_property

    A single realisation of three-dimensional Brownian motion for times 0 ≤ t ≤ 2. Brownian motion has the Markov property, as the displacement of the particle does not depend on its past displacements. In probability theory and statistics, the term Markov property refers to the memoryless property of a stochastic process, which means that its ...

  3. Memorylessness - Wikipedia

    en.wikipedia.org/wiki/Memorylessness

    The memorylessness property asserts that the number of previously failed trials has no effect on the number of future trials needed for a success. Geometric random variables can also be defined as taking values in N 0 {\displaystyle \mathbb {N} _{0}} , which describes the number of failed trials before the first success in a sequence of ...

  4. Geometric distribution - Wikipedia

    en.wikipedia.org/wiki/Geometric_distribution

    The geometric distribution is the only memoryless discrete probability distribution. [4] It is the discrete version of the same property found in the exponential distribution. [1]: 228 The property asserts that the number of previously failed trials does not affect the number of future trials needed for a success.

  5. Bernoulli process - Wikipedia

    en.wikipedia.org/wiki/Bernoulli_process

    Much of what can be said about the Bernoulli process can also be generalized to more than two outcomes (such as the process for a six-sided die); this generalization is known as the Bernoulli scheme. The problem of determining the process, given only a limited sample of Bernoulli trials, may be called the problem of checking whether a coin is fair.

  6. Markov chain - Wikipedia

    en.wikipedia.org/wiki/Markov_chain

    A Markov process is a stochastic process that satisfies the Markov property (sometimes characterized as "memorylessness"). In simpler terms, it is a process for which predictions can be made regarding future outcomes based solely on its present state and—most importantly—such predictions are just as good as the ones that could be made ...

  7. Shewhart individuals control chart - Wikipedia

    en.wikipedia.org/wiki/Shewhart_individuals...

    [3]: 43 Points outside of these control limits are signals indicating that the process is not operating as consistently as possible; that some assignable cause has resulted in a change in the process. Similarly, runs of points on one side of the average line should also be interpreted as a signal of some change in the process.

  8. Queueing theory - Wikipedia

    en.wikipedia.org/wiki/Queueing_theory

    M stands for "Markov" or "memoryless", and means arrivals occur according to a Poisson process; D stands for "deterministic", and means jobs arriving at the queue require a fixed amount of service; k describes the number of servers at the queueing node (k = 1, 2, 3, ...) If the node has more jobs than servers, then jobs will queue and wait for ...

  9. Markov decision process - Wikipedia

    en.wikipedia.org/wiki/Markov_decision_process

    Markov decision process (MDP), also called a stochastic dynamic program or stochastic control problem, is a model for sequential decision making when outcomes are uncertain. [ 1 ] Originating from operations research in the 1950s, [ 2 ] [ 3 ] MDPs have since gained recognition in a variety of fields, including ecology , economics , healthcare ...

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