Calculate CI for Var of sum of normally dist variables?

#1
Hi guys,

I'm trying to figure out how to calculate a confidence interval for a variable that is the sum of normally distributed variables.

y=u+t+e

u=constant, t-N(0,var(t)), e-N(0,var(e)), y-N(u,var(t)+var(e))
dof(t) = 3, dof(e) = 16

How do I calculate a confidence interval for var(y)?

Best regards,
Patrick Carlberg