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Given an infinite sequence of infinite strings, where each character of each string is chosen uniformly at random, any given finite string almost surely occurs as a prefix of one of these strings. Both follow easily from the second Borel–Cantelli lemma. For the second theorem, let E k be the event that the kth string begins with the given text.
Serial reaction time (SRT) is a commonly used parameter in the measurement of unconscious learning processes. [1] This parameter is operationalised through a SRT task, in which participants are asked to repeatedly respond to a fixed set of stimuli in which each cue signals that a particular response (i.e., button press) needs to be made.
This association facilitates the identification and the calculation of probabilities of the events. Random variables can appear in random sequences. A random process is a sequence of random variables whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions.
Randomization is not haphazard; instead, a random process is a sequence of random variables describing a process whose outcomes do not follow a deterministic pattern but follow an evolution described by probability distributions. For example, a random sample of individuals from a population refers to a sample where every individual has a known ...
The concept generally relies on the notion of a sequence of random variables and many statistical discussions begin with the words "let X 1,...,X n be independent random variables...". Yet as D. H. Lehmer stated in 1951: "A random sequence is a vague notion... in which each term is unpredictable to the uninitiated and whose digits pass a ...
The term Bernoulli sequence is often used informally to refer to a realization of a Bernoulli process. However, the term has an entirely different formal definition as given below. Suppose a Bernoulli process formally defined as a single random variable (see preceding section). For every infinite sequence x of coin flips, there is a sequence of ...
If you and your friends have been craving a trivia night, this set of questions and answers is for you. No need to scrounge up a set of trivia cards — this post has plenty of random trivia ...
In a "truly" random sequence of numbers of sufficient length, for example, it is probable there would be long sequences of nothing but repeating numbers, though on the whole the sequence might be random. Local randomness refers to the idea that there can be minimum sequence lengths in which random distributions are approximated. Long stretches ...