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
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.
You should reread what Moo told you.
Start with..Write down the joint pdf of , 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.
Here's some more calc 3...
And this should be outlined in you stat book too.