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## Homework Statement

X ~ [itex]N(2,9)\\[/itex]

Y ~ [itex]\chi_9^2\\[/itex]

Z ~ [itex]\dfrac{X-2}{3}\\[/itex]

What is [itex]\dfrac{X-2}{\sqrt{Y}}\\[/itex]

What is [itex]\dfrac{9Z^2}{Y}\\[/itex]

## Homework Equations

## The Attempt at a Solution

I'm not sure about [itex]\dfrac{X-2}{\sqrt{Y}}[/itex], maybe a standard normal, but I'm just guessing.

And for [itex]\dfrac{9Z^2}{Y}[/itex], I'm pretty sure that would be distributed as a [itex]t_9[/itex] since a standard normal over a the square root of a chi squared should be a t distribution?

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