No " sample space " is involved in my first observation; it's just a fact of arithmetic, involving no probability.
32.
Of course, the choice of sample space is a subjective decision, but that doesn't stop me from having an opinion.
33.
This means the sample space ? must consist of all possible infinite sequences of " H " or " T ":
34.
Since spatial resolution depends on the tip-sample spacing, smaller tip-sample spacings and higher topographic resolution blur the features in tunneling spectra.
35.
This algorithm proceeds by randomly attempting to move about the sample space, sometimes accepting the moves and sometimes remaining in place.
36.
In that context, a random variable is understood as a function defined on a sample space whose outputs are numerical values.
37.
An IID sequence does not imply the probabilities for all elements of the sample space or event space must be the same.
38.
The Dirac measure is a probability measure, and in terms of probability it represents the almost sure outcome in the sample space.
39.
For example, I may define the sample space for a fair coin-toss to be { H, T } for Heads and Tails.
40.
This mathematical definition of probability can extend to infinite sample spaces, and even uncountable sample spaces, using the concept of a measure.
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