is a standard normal random variable. Show that the PDF of is

I've tried thisloadsof times but I can't get anywhere near the answer (Worried)

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- Nov 26th 2009, 05:51 PMchella182Transforming the Normal distribution
*is a standard normal random variable. Show that the PDF of is*

I've tried this**loads**of times but I can't get anywhere near the answer (Worried) - Nov 26th 2009, 06:17 PMmatheagle
I've already shown you the technique.

Why don't you post what you've done and we can find what's wrong.

There's a basic formula in most books for 2-1 transforms, so all you have to do is plug into that.

I'm sure you can find it online, but it's easy to do it from scratch. - Nov 27th 2009, 01:59 AMchella182
I know you have, and I tried applying that (along with using a similar example we had in our notes) but didn't get anywhere near the required answer (that I'm aware of). I'll just type exactly what I've written.

That's practically identical to what we wrote for the example in our notes. Then we wrote

Then I've got that so

And then this is where I start going off miles away from the answer. - Nov 27th 2009, 07:59 AMmatheagle
no, look at your start

But that seems to be a typo

However the next line is wrong too

means

AS I already said, its a 2 to 1 transformation. - Nov 27th 2009, 09:50 AMmatheagle
I'll fix your error...

now continue

NOW plug into the normal and differentiate - Nov 28th 2009, 08:51 AMchella182
I know, isn't the same as (Worried) it was indeed a typo :p was trying to be quick 'cause the homework was due in on the day I replied. It was an unassessed question so it didn't matter really, was just intrigued.