Restricting a distribution with infinite support to a bounded interval

Question

I need to restrict a Gaussian distribution to the bounded interval $[0,1]$. Is there a way to systematically scale the pdf values to carry out this restriction?

Answer 1

Hint: This is the so called truncated normal distribution. The pdf is

$$f(x;\mu,\sigma,a,b) = \frac{1}{\sigma}\, \frac{\phi(\frac{x - \mu}{\sigma})}{\Phi(\frac{b - \mu}{\sigma}) - \Phi(\frac{a - \mu}{\sigma}) },$$

where $a$ is the lower bound and $b$ is the upper bound of the interval. $\phi(\cdot )$ is the pdf of the and $\Phi(\cdot )$ the cdf of the standard normal distribution. In your case $a=0$ and $b=1$