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<< RANDOM DISTRIBUTIONS >>

The Transformation Method

Consider a collection of variables {x1, x2, x3, ...} that are distributed according to the function Px(x), then the probability of finding a value that lies between x and x+dx is
Px(x)dx. If y is some function of x then we can write:

where Py(y) is the probability density that describes the collection {y1, y2, y3, ...}.

Px(x) = C (i.e. Uniform)
and so Py(y) = C |dx/dy|