Let \(F_{0}(t)=1-e^{-\lambda t}\) , where \(\lambda\) >0.

a.) show that \(S_{x}t=e^{-\lambda t}\)

b.) show that \(\mu_{x}=\lambda\)

c.) show that \(e_{x}=(e^{\lambda}-1)^{-1}\)

d.) What conclusions do you draw about using this lifetime distribution to model human mortality?