9 lines
541 B
Markdown
9 lines
541 B
Markdown
# Topic 1
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## Probability Theory under Language of Measure Theory
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### Uniform random numbers
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Define picking a random number from the interval $[0,1]$ form the uniform probability distribution.
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As a function $f:[0,1]\to S$, where $S$ is the space of potential outcomes of a random phenomenon. (Note, this definition inverts the axis of "probability" and "event" so that we can apply the measure theory to probability theory. Before, we define the probability of an event as a function $P:S\to [0,1]$, where $S\in A$ and $\int_A P(x)dx=1$.) |