If X∼Uniform(a,b)X \sim \text{Uniform}(a, b)X∼Uniform(a,b), what is the Moment Generating Function MX(t)M_X(t)MX(t) for t≠0t \neq 0t=0?
etb−etat(b−a)\frac{e^{tb} - e^{ta}}{t(b-a)}t(b−a)etb−eta
eta−etbt(b−a)\frac{e^{ta} - e^{tb}}{t(b-a)}t(b−a)eta−etb
et(b−a)t\frac{e^{t(b-a)}}{t}tet(b−a)
et(a+b)/2e^{t(a+b)/2}et(a+b)/2