# Thread: Derivative of Standard Normal Random Variable

1. ## Derivative of Standard Normal Random Variable

Hi guys,
I have 2 problems that are kind of confusing me.
The assumptions are the same for both.
Help on either of them would be appreciated

Let 'z' be a standard normal random variable. Let '\phi ' be the
standard normal pdf and '\Phi ' be the standard normal cdf.

1. Show that $\frac{\mathrm{d} \phi(z)}{\mathrm{d}z}= -z \phi (z)$

2. Show that $\frac{\mathrm{d} \lambda(z)}{\mathrm{d}z}= \lambda ^2(z) - z\lambda (z)$

Where $\lambda (z) = \phi (z) / 1 - \Phi (z)$

I'm not sure if this would fit better here in calculus or in statistics, please tell me if I should put it in statistics.

2. Originally Posted by statisticsjoe
Hi guys,
I have 2 problems that are kind of confusing me.
The assumptions are the same for both.
Help on either of them would be appreciated

Let 'z' be a standard normal random variable. Let '\phi ' be the
standard normal pdf and '\Phi ' be the standard normal cdf.

1. Show that $\frac{\mathrm{d} \phi(z)}{\mathrm{d}z}= -z \phi (z)$

2. Show that $\frac{\mathrm{d} \lambda(z)}{\mathrm{d}z}= \lambda ^2(z) - z\lambda (z)$

Where $\lambda (z) = \phi (z) / 1 - \Phi (z)$

I'm not sure if this would fit better here in calculus or in statistics, please tell me if I should put it in statistics.
What have you tried? Where are you stuck?

And please use the tags [img]http://latex.codecogs.com/png.latex? and [/img] to open and close latex (until the known site problems with the latex compiler are fixed). Oherwise your equations cannot be easily read or understood.