Question: The lognormal distribution, on which Example 2.3.10 is based, has an interesting property. If we have the pdf then Exercise 2.35 shows that all moments

The lognormal distribution, on which Example 2.3.10 is based, has an interesting property. If we have the pdf
The lognormal distribution, on which Example 2.3.10 is based, has

then Exercise 2.35 shows that all moments exist and sire finite. However, this distribution does not have a moment generating function, that is,

The lognormal distribution, on which Example 2.3.10 is based, has

does not exist. Prove this.

-(log )2 /2, 0 1( 00, , dz

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