# Exercise Solution 3.41

By [3.143], the moment generating function of *Y* is:

[s1]

[s2]

[s3]

[s4]

The second moment *E*(*Y*^{2}) 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.

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