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Say I have a function function $f(x)$ returning any real between 0 and 1, for a $x$ between 0 and 1.

I want to get $n$ randomly generated values of $x$, based the probablity they occur from $f(x)$.

Example: If $n=5$, and $f(x)$ described a direct ascending line from 0 to 1, I could get $x_1=0.8$, $x_2=0.7$, $x_3=0.75$, $x_4=0.4$, $x_5=0.3$.

Basically, the higher $f(x)$, the more the random value tends to $x$.

Any idea how to achieve that?

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    @GerryMyerson More values tend to to be located at the end of $f(x)$ (i.e., towards 1), because $f(x)$ is ascending.2012-01-16

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I think I finally understand the question: you want $n$ samples from a random variable whose probability density function is (proportional to) $f(x)$. There is a lot of literature on this problem, and now that I have given you the keywords and keyphrases to look for, you may be able to find what you need and report back to us.