Exercise Solution 3.41
By [3.143], the moment generating function of Y is:
[s1]
[s2]
[s3]
[s4]
The second moment E(Y2) of Y is obtained as the second derivative of MGF [s4] evaluated at w = 0:
[s5]
[s6]
[s7]
[s8]
where [s7] is obtained by taking the derivative in [s6] and then taking a limit as w → 0, which requires applying l’Hôpital’s rule twice.