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**Statistik** Hi,

I have a 3-part question from an exam I took and did not solve correctly. I'd love to find out what I should have done... (We already received the exam back, I'm "cleaning up" loose ends.) Thank you!

Assuming Y1, Y2, ..., Yn are iid Exp(1)

a) What are the mean, variance (sigma squared) and third and fourth central moments? (We were given the hint to prove $\displaystyle EY^k = k! $)

b) Find $\displaystyle E(\bar Y_n)^2 $ and $\displaystyle ES_n^4 $

c) Find $\displaystyle Ee^{-Y_{(k)}} $