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Two business partners carry 15 year term life insurance. The insurer pays 100, 000 for each partner who dies?

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Life Insurance

Two business partners carry 15 year term life insurance. The insurer pays 100, 000 for each partner who dies within 15 years, and 0 for each partner who does not die within 15 years. The remaining lifetimes of the two partners are independent and each are uniformly distributed on [0, 15]. Determine the moment generating function of the total amount the insurer pays for the partners.

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