For 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)?
etb−etat(b−a)\frac{e^{tb} - e^{ta}}{t(b-a)}t(b−a)etb−eta
et(b−a)t\frac{e^{t(b-a)}}{t}tet(b−a)
etb+eta2\frac{e^{tb} + e^{ta}}{2}2etb+eta
1b−a∫abetxdx\frac{1}{b-a} \int_a^b e^{tx} dxb−a1∫abetxdx