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At the same time, the probability that the sequence contains a particular subsequence (such as the word MONKEY, or the 12th through 999th digits of pi, or a version of the King James Bible) increases as the total string increases. This probability approaches 1 as the total string approaches infinity, and thus the original theorem is correct.
The Dirac delta function, although not strictly a probability distribution, is a limiting form of many continuous probability functions. It represents a discrete probability distribution concentrated at 0 — a degenerate distribution — it is a Distribution (mathematics) in the generalized function sense; but the notation treats it as if it ...
The quantum-mechanical "Schrödinger's cat" paradox according to the many-worlds interpretation.In this interpretation, every quantum event is a branch point; the cat is both alive and dead, even before the box is opened, but the "alive" and "dead" cats are in different branches of the multiverse, both of which are equally real, but which do not interact with each other.
If the cat is in the first box and the mouse is in the fifth, the probability that the cat will be in box two and the mouse will be in box four after the timer advances is one. The cat eats the mouse if both end up in the same box, at which time the game ends. Let the random variable K be the time the mouse stays in the game.
Some state departments of insurance allow insurers to use cat modeling in their rate filings to help determine how much premium their policyholders are charged in catastrophe-prone areas. Insurance rating agencies such as A. M. Best and Standard & Poor's use cat modeling to assess the financial strength of insurers that take on catastrophe risk.
A thought experiment called Schrödinger's cat illustrates the measurement problem. A mechanism is arranged to kill a cat if a quantum event, such as the decay of a radioactive atom, occurs. The mechanism and the cat are enclosed in a chamber so the fate of the cat is unknown until the chamber is opened.
The probability distribution of the sum of two or more independent random variables is the convolution of their individual distributions. The term is motivated by the fact that the probability mass function or probability density function of a sum of independent random variables is the convolution of their corresponding probability mass functions or probability density functions respectively.
Computerized adaptive testing (CAT) is a form of computer-based test that adapts to the examinee's ability level. For this reason, it has also been called tailored testing . In other words, it is a form of computer-administered test in which the next item or set of items selected to be administered depends on the correctness of the test taker's ...