Let the independent random variables X1 and X2 be N(0,1) and , respectively. Ley and Y2=X2.

a) Find the joint pdf of Y1 and Y2

b) Determine the marginal pdf of Y1 and show that Y1 has a t distribution

Thanks!

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- May 18th 2009, 09:11 AMjennifer1004joint / marginal pdf
Let the independent random variables X1 and X2 be N(0,1) and , respectively. Ley and Y2=X2.

a) Find the joint pdf of Y1 and Y2

b) Determine the marginal pdf of Y1 and show that Y1 has a t distribution

Thanks! - May 18th 2009, 09:31 AMMoo
Hello,

I assume it's ?

Write down the joint pdf of , which is just the product of their pdf (because they're independent)

Then, you can see that (because )

And then make the transformation

Also, don't forget to divide by the Jacobian !

that's pretty "long" to do, so it'd be good for you and for us that you show what you've tried/done, what you want us to correct. - May 18th 2009, 02:35 PMmatheagle
This is okay. At first I thought you had two indep st. normals.

You need this to be a .

I was lost on that missing subscript at first.

The joint density of Y1 and Y2 should factor giving you independence. - May 20th 2009, 06:55 PMjennifer1004
I'm sorry. It is supposed to be and I haven't a clue where to begin. Thanks

- May 27th 2009, 05:18 PMjennifer1004
Is this anywhere near what I am supposed to do?

Thanks!

Attachment 11650 - May 27th 2009, 05:38 PMmatheagle
(3) is way off. you need to review jacobians from calculus 3.

- May 27th 2009, 05:41 PMjennifer1004
Thank you. I just have my statistics book though. Could you help point me in the right direction? I don't know what I did wrong based on my text.

- May 27th 2009, 05:48 PMmatheagle
You should reread what Moo told you.

Start with..Write down the joint pdf of http://www.mathhelpforum.com/math-he...6bc02d44-1.gif, which is just the product of their pdf ..

then obtain the jacobian and change variables.

Here's a review that explains the change for polar, but it's the same idea.

http://www.maths.abdn.ac.uk/~igc/tch...es/node77.html

Here's some more calc 3...

http://tutorial.math.lamar.edu/Class...Variables.aspx

And this should be outlined in you stat book too.