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Exact(15)
Let X be the set of all sequences of outcomes of a binary process.
The set of all infinite binary sequences of outcomes is known as the Cantor space.
Yet ordinarily we are happy to characterise even quite small finite sequences of outcomes as random.
For some but only some types of goods, improving sequences of outcomes are preferred to declining sequences.
Let X<ω be the set of finite sequences of outcomes of a binary process, or strings.
So on the standard account of randomness, no sequences of outcomes of a biased chance process are random, but of course these outcomes happened by chance.
Similar(45)
Subjects observed the sequence of outcomes but not the underlying regime process.
Consider some particular sequence of outcomes en that results from observations cn.
The number of balls is sufficiently large that the sequence of outcomes of draws is long enough to be random.
For if a world contains a genuinely random sequence of outcomes, there will be no short description of that sequence.
So the sequence of outcomes for the baker's transformation (under this partition) is a random sequence.
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