Show that if y, has a x distribution with v degrees of freedom and Y has a distribution with v degrees of freedom, then U = Y + Y has a x distribution with v + v degrees of freedom, provided that Y and Y are independent. The moment-generating function for Y is my, (t) = and the moment-generating function for Y is .Since Y, and Y are independent, the moment-generating function for U is m(t) = which is the moment-generating function for a x2 distribution with v + v degrees of freedom.