Generate random results in a continuous field

Question

How can we generate random results for a field like economical predictions where there is no limited number of results (contrary to a coin with 2 results) and also contrary to a random walk with steps with a fixed length (in either direction).

Answer 1

To generate a numeric random variable onehas to know its distribution. The simple case of a uniform random variable in $[0,1]$ can be simulated as follows: Mark a point on the boundary of a circular spinning top with perimeter length $1$ and let it spin. Once it lands, measure the clockwise distance from the mark to the landing point. For other continuous distributions, one can use such a uniform random variable as input and use the inverse function of the cumulative distribution function to produce a random variable with that distribution. Many othr methods are known especially for specific distributions such as the normal distribution, especially suitable for computer programs.