This is what I'm supposed to prove...
Suppose that $Y$ and $Z$ are independent random variables with $Y \sim z^2(v)$, and $Z \sim N(0,1)$, and $T = \frac{Z}{\sqrt{\frac{Y}{v}}}$. Let $X = T^2$. Prove that $X \sim f(1,v)$.
How would I start to prove this?
I know I should be using the theorem that states: If $U$ and $V$ are independent variable having square distribution with $V_1$ and $V_2$ degrees of freedom then $$F= \frac{\frac{U}{V_1}} {\frac{V}{V_2}}$$ is a random variable having an $F$ distribution for $f > 0$ and $g(f) = 0$ elsewhere.