I need to bound a 1D gaussian/normal (or similar) probability density function in the domain interval $[-3\sigma, 3\sigma]$ in a way that still integrates to 1. I would need something like this:
$ p(x) = \begin{cases} N(x;\mu, \sigma) &\text{if } -3\sigma \leq x \leq 3\sigma\\ 0 & \text{otherwise } \end{cases} $
This is NOT a probability density function but how could I get a bounded distribution that is similar to the gaussian case?
Thanks in advance,
Federico