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The term strong Markov property is similar to the Markov property, except that the meaning of "present" is defined in terms of a random variable known as a stopping time. The term Markov assumption is used to describe a model where the Markov property is assumed to hold, such as a hidden Markov model .
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 ...
It is the continuous analogue of the geometric distribution, and it has the key property of being memoryless. [2] In addition to being used for the analysis of Poisson point processes it is found in various other contexts. [3] The exponential distribution is not the same as the class of exponential families of distributions.
For instance, =,, could be defined to represent the state where there is one quarter, zero dimes, and five nickels on the table after 6 one-by-one draws. This new model could be represented by 6 × 6 × 6 = 216 {\displaystyle 6\times 6\times 6=216} possible states, where each state represents the number of coins of each type (from 0 to 5) that ...
We will assume for the moment that all state spaces of the systems considered, classical or quantum, are finite-dimensional. The memoryless in the section title carries the same meaning as in classical information theory: the output of a channel at a given time depends only upon the corresponding input and not any previous ones.
The survival function is one of several ways to describe and display survival data. Another useful way to display data is a graph showing the distribution of survival times of subjects. Olkin, [5] page 426, gives the following example of survival data. The number of hours between successive failures of an air-conditioning (AC) system were recorded.
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 ...
One common form of implicit MDP model is an episodic environment simulator that can be started from an initial state and yields a subsequent state and reward every time it receives an action input. In this manner, trajectories of states, actions, and rewards, often called episodes may be produced.