# Moment Generating Function exercises: Knowing that $M_{X}(0)=1$ and $M´_{X}(0)= EX$

Hi guys,

Any help with letter b of this exercise from Casella´s Book?

I could finish the letter a). But I cant move in letter b).

Any help?

Thanks

• Hint: (b) implies that $M_X'(0)<0$, so that $M_X(t^*)=c<1$ for some $t^*$ near $t=0$. – Alex R. Feb 7 at 21:00
• @AlexR. So, Its just apply $t^{*}$ round zero, right? I will have: $P(S_{n} > a) < \exp(-a.0)[M_{X}(t^{*})]^{n} = 1 . c^{n}$. – Laura Feb 7 at 21:09