Let X∼Exp(λ)X \sim \text{Exp}(\lambda)X∼Exp(λ). What is the MGF of XXX?
\frac{\lambda}{\lambda-t} \text{ for } t < \lambda
\frac{\lambda}{\lambda+t} \text{ for } t > -\lambda
e^{\lambda t}
\frac{t}{\lambda-t}