(Solution) - The lognormal distribution on which Example 2 3 10 is based has -(2025 Original AI-Free Solution)

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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 exist and sire finite. However, this distribution does not have a moment generating function, that is,

does not exist. Prove this.