The cumulative distribution function \Phi : \mathbb {R}\to \mathbb {R} of the standard normal \mathcal{N}(0,1) can be written as

Question

\Phi (z) = \int _{A}^{B(z)} \frac{1}{\sqrt{2 \pi }} e^{C(x)} \, dx

where B(z) is a function of z and C(x) is a function of x. Write down the integration limits A,B(z),\, as well as the function \, C(x) in the integrand.

Enter inf for \infty.

A=\quad
unanswered

B=\quad
unanswered

C=\quad

Answer 1

A=-\infty
B(z)=z
C(x)=-\frac{x^2}{2}