I had a homework problem which I'm having trouble with. Unfortunately I missed my class when the teacher was giving examples of t-distribution problems. If someone could help me about the steps involving to solve this problem, I would really appreciate it. Let T=K(X+Y)/(Z^2 + W^2)^1/2 where X,Y,Z and W are independent normal variables with mean 0 and variance >0. Find the value of K so that T has a student's t distribution. How many degrees of freedom does T have? One of my friends had told me that K=1 and (d.o.f.) n=2 for T, but unable to give a proper explaination of how he got it. I just want to know the steps to solve this. Thank you.