Truncated normal random variable Find the cdf and quantile function for the truncated (at a) normal random variable given that $$\frac{\varphi(x) I_{x>a}}{1-\Phi(a)}$$ where $\varphi(x)$ is the density for standard normal and $\Phi(x)$ is the cdf for standard normal distribution. Express answers in terms of $\varphi(x)$ and $\Phi(x)$.
Appreciate your help, thank you!

Since the cdf is $F_t (u)=\int_a^u\frac{\varphi(x) }{1-\Phi(a)} dx$, it can be expressed in terms of normal and hence standard normal (using the substitution $v=x-a $ to 'evaluate' the integral).
