Showing $\Phi^{-1}(x) = - \Phi^{-1}(1-x)$ for a normal distribution

29 Views Asked by At

Let $\Phi$ be the CDF of a normal random variable. Let $x \in (0,1)$. Why do we have $$\Phi^{-1}(x) = - \Phi^{-1}(1-x)?$$