When Y,,Y,,.,Y, is a random sample from N(u,0), we learned in class that the Y - u has t distribution with n-1 degrees of freedom, where Y and S are S n-1 statistic T = the sample mean and sample...

Extracted text: When Y,,Y,,.,Y, is a random sample from N(u,0), we learned in class that the Y - u has t distribution with n-1 degrees of freedom, where Y and S are S n-1 statistic T = the sample mean and sample standard deviation, respectively. Write out the form of T? and show algebraically that T2 can be written as the ratio of two independent x² random variables, each divided by their respective degrees of freedom. What is, therefore, the distribution of T?