Mathematica: How to compile the following code (sampling from a distribution)?

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Peter Schneider
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How to compile the following code (sampling from a distribution)?
I hope you found a solution that worked for you :)
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(mathematica.stackexchange.com/users/41058/john-taylor)John Taylor
(mathematica.stackexchange.com/users/19758/jimb)JimB
A special thanks goes out to the (mathematica.stackexchange.com/questions/301448/how-to-compile-the-following-code-sampling-from-a-distribution)Stackexchange community

I wish you all a wonderful day! Stay safe :)
If anything is off, please write me at peter D.O.T schneider A.T ois42.de

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sampling
compile
random