Does anyone know where i can find the PDF for the the following Z:

Z = (X^2) / (Y^2), X and Y are zero mean Gaussian variables with standard deviations sigma_x and signma_y (X, Y independent and uncorrelated).

I know that X^2 and Y^2 are chi-squared but i have not been able to find a PDF of their ratio

Also, is there a formula for:

E{Z} and Var{Z}.

Many thanks for any help

cheers

Tim