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How do I sample RANDOMLY from a known probability distribution?
There are numerous mathematical methods. In example:
Inversion theorem
Let x be a continuous random variable distributed over the interval [a, b] with a
probability density function f(x) and a cumulative probability distribution
function F(x) that is invertible. Given a random number, r, in the interval [0, 1],
a value x
*
of x can be randomly selected according to:
Let x be a discrete random variable taking N values, x
i
of probability, P
i
so that:
Given a random number, r, in the interval [0, 1], a value x
*
of x can be randomly
selected according to:
x
*
= x
j
where j= min{ j:
}
The MC method …