How to generate random numbers with a known distribution of f(X)=(8X^2 + 1)*Exp( -X^2 )

[laoda]

Dear All,

I need to simulate a random number generator which can generate numbers X with the probability distribution of 

 f (X) = ( 8X^2 + 1)*Exp ( -X^2 ).

This distribution is not a common distribution.

I have searched a lot, but I still do not know how to realize it.

Any help on this topic would be highly appreciated.

[Henrik_Volkers]

Make a lookup table of the integral of your function (normalized to 1)

Use the rectangle random generator and pipe that value through the lookup table, scale it ... voila.