Poissom (homework help)

Hello everyone, bellow are some of the exercises I need to complete and I have a couple of questions about them





- In 2.1 how can moment generating functions help me prove that

- With regards to 2.2 I have no clue on how to go about proving that. What am I looking at


Sorry if the exercises are poorly translated, English is not my first language.

Thanks !

pretty please with sugar on top?