My math is quite limited so please bear with me. I will get to the point: Is there a way to transform a continuous function into a bounded one?
In essence I have a normalized Gaussian distribution defined by:
$y = b + \frac{a}{c\sqrt{\frac{\pi}{2}}} \cdot e^{\frac{-2(x-d)^2}{c^2}}$
I am only interested in values of $y$ for $0 \leq x \leq 500$. a,b,c and d are parameters.
I would like to maintain the ability of the curve to be a normalised probability distribution but only for $0 \leq x \leq 500$.
Is there a way of doing this or am I trying the impossible?
Thanks to anyone that can render assistance.