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Update Math401_T1.md

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Zheyuan Wu
2025-06-14 16:27:52 -05:00
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Define picking a random number from the interval $[0,1]$ form the uniform probability distribution.
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 $\int_A P(x)dx=1$.)
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 $\int_A P(x)dx=1$.)
$\ket{1}= \begin{pmatrix} 1 \\ 0 \end{pmatrix}$ is a vector in a Hilbert space.