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 → 0, which requires applying l’Hôpital’s rule twice.

 

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