541 B
541 B
Topic 1
Probability Theory under Language of Measure Theory
Uniform random numbers
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.)