Let X∼Uniform(0,1)X \sim \text{Uniform}(0, 1)X∼Uniform(0,1). What is the MGF of XXX?
et−1t\frac{e^t - 1}{t}tet−1
ete^tet
11−t\frac{1}{1-t}1−t1
1+t1+t1+t