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While studying Mathematical statistics through "Introduction to Mathematical Statistics 7th" (by Hogg and Craig), I've been stuck in the Theorem above. The answer of the exercise 7.5.8 is not given in the manual solution and even not on Slader! "https://www.slader.com/textbook/9780321795434-introduction-to-mathematical-statistics/401/"

Can anyone help me?

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    $\begingroup$ Please add the self-study tag and detail your attempt(s) at solving the question. $\endgroup$ – Xi'an Dec 27 '19 at 7:14
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Hint: the moment generating function is a natural tool for the study of exponential families.

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