Please answer all parts as best as you can :)

(45 points) Let X have the density function given by mega9'\" , :1: > 0 fx(m)={ O , 0.11). where 6 > 0 is a constant. 1. (15 points) Show/prove that the moment-generating function for X is M X(t) = ()2.(With details) 2. (15 points) Let U 2 2X + 1, nd the moment-generating function My(t) of U. 3. (15 points) Calculate E(U)