Let say that X ~ Beta(c,d) or X~N(mu,sigma^2) or anything really... does T(a)Xa also

have a beta/Normal distribution??? Where a is just a vector. What if T(a)a = 1?? Is there a way to work out its distribution??

Thanks for the help!

Note: T(a) = transpose of vector a, i don't know how to do those superscript t's on here....