LetX1,X2,...,X n be a sequence of independent and identically distributed random variables having the Exponential(λ) distribution,λ >0, f Xi (x) ={λe −λx , x >0 0, otherwise (a) Show that the moment...

LetX1,X2,...,X_n
be a sequence of independent and identically distributed random variables having the Exponential(λ) distribution,λ >0,

f_Xi(x) ={λe^−λx, x >0

0, otherwise

(a) Show that the moment generating function m_X(s) :=E(e^sX) =λ/(λ−s) for   s<>