Search results
Results from the WOW.Com Content Network
The only continuous random variable that is memoryless is the exponential random variable. It models random processes like time between consecutive events. [8] The memorylessness property asserts that the amount of time since the previous event has no effect on the future time until the next event occurs.
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 ...
In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate; the distance parameter could be any meaningful mono-dimensional measure of the process, such as time ...
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 ...
For an exponential survival distribution, the probability of failure is the same in every time interval, no matter the age of the individual or device. This fact leads to the "memoryless" property of the exponential survival distribution: the age of a subject has no effect on the probability of failure in the next time interval.
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.
Residual time. In the theory of renewal processes, a part of the mathematical theory of probability, the residual time or the forward recurrence time is the time between any given time and the next epoch of the renewal process under consideration. In the context of random walks, it is also known as overshoot.
For example, if the renewal process is modelling the numbers of breakdown of different machines, then the holding time represents the time between one machine breaking down before another one does. The Poisson process is the unique renewal process with the Markov property , [ 1 ] as the exponential distribution is the unique continuous random ...