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  2. 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 ...

  3. Exponential distribution - Wikipedia

    en.wikipedia.org/wiki/Exponential_distribution

    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 ...

  4. Markov property - Wikipedia

    en.wikipedia.org/wiki/Markov_property

    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 .

  5. Renewal theory - Wikipedia

    en.wikipedia.org/wiki/Renewal_theory

    The Poisson process is the unique renewal process with the Markov property, [1] as the exponential distribution is the unique continuous random variable with the property of memorylessness. Renewal-reward processes

  6. Survival function - Wikipedia

    en.wikipedia.org/wiki/Survival_function

    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.

  7. Residual time - Wikipedia

    en.wikipedia.org/wiki/Residual_time

    This is a known characteristic of the exponential distribution, i.e., its memoryless property. Intuitively, this means that it does not matter how long it has been since the last renewal epoch, the remaining time is still probabilistically the same as in the beginning of the holding time interval.

  8. Puzzle solutions for Saturday, Nov. 30, 2024

    www.aol.com/news/puzzle-solutions-saturday-nov...

    Note: Most subscribers have some, but not all, of the puzzles that correspond to the following set of solutions for their local newspaper. CROSSWORDS

  9. Markovian arrival process - Wikipedia

    en.wikipedia.org/wiki/Markovian_arrival_process

    A Markov arrival process is defined by two matrices, D 0 and D 1 where elements of D 0 represent hidden transitions and elements of D 1 observable transitions. The block matrix Q below is a transition rate matrix for a continuous-time Markov chain.