Let M(z) be the m.g.f. of a r.v. X such that E{X} = 1. Is it true

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Let M(z) be the m.g.f. of a r.v. X such that E{X} = 1. Is it true that M(z) ≥ 1 for all z ≥ 0? Answer the same question for the case E{X} = −1.

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