Let $X$ be a random variable having standard normal distribution. Let $\Phi$ denote its distribution function. Find
$$ \int_0^\infty \operatorname{Prob} (\Phi(X) \geq u) \; du $$
Let $X$ be a random variable having standard normal distribution. Let $\Phi$ denote its distribution function. Find
$$ \int_0^\infty \operatorname{Prob} (\Phi(X) \geq u) \; du $$