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Claim amounts on a certain type of insurance policy follow an exponential distribution with a mean of 100. The insurance company purchases a special type of reinsurance policy so that for a given claim X, the reinsurance company pays:0 < X < 80: 0.5X - 4080 < X < 160: X - 120X ≥ 160: 0Calculate the expected amount paid by the reinsurance company on a randomly chosen claim.
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