I am trying to wrap my head around the connections between the standard Normal distribution and the error function. I could use some help working through the following problem.
Show that the following conversion between $\Phi$ and erf holds for all z:
$\Phi(z) = \frac{1}{2} +\frac{1}{2}erf(\frac{z}{\sqrt{2}})$
The second part of this question asks to show that erf is an odd function. I am new to the normal distribution and don't really know where to start. Any and all help is appreciated.