Suppose we form a sample variance

from a sequence of IID Gaussian random variables and then form another sample variance

from a different sequence of IID Gaussian random variables that are independent from the first set. We wish to determine if the true variances of the two sets of Gaussian random variables are the same or if they are significantly different, so we form the ratio of the sample variances

to see if this quantity is either large or small compared to 1. Assuming that the X_K and the Y_K are both standard normal, find the PDF of the statistic and show that it follows an F distribution.