How can we generate a sample in the interval $[a,b]$ based on a Gaussian distribution?
If we have a Gaussian random generator, just by mapping the number to the range and pruning (ignoring) the values outside of the range, does our sample still follow the Gaussian distribution? In short, how correct is this approach?
added later : assume we can generate $\mathcal N(\mu, \sigma^2)$ with any parameters, now with given [a,b] , is there a way to chose a relatively good $\mathcal (\mu)$ and $\mathcal (\sigma)$ ? for example $\mathcal \mu = (a+b)/2$ & $\mathcal \sigma = (b - \mu)/3$