Let X∼Uniform(0,1)X \sim \text{Uniform}(0, 1)X∼Uniform(0,1). What is the MGF MX(t)M_X(t)MX(t)?
et−1t\frac{e^t - 1}{t}tet−1
1−ett\frac{1 - e^t}{t}t1−et
et−1e^t - 1et−1
ett\frac{e^t}{t}tet