Question: A paper machine operates 100 days by expectation before malfunctioning, and repairs take 10 days by expectation. Operation and repair times are mutually independent and

A paper machine operates 100 days by expectation before malfunctioning, and repairs take 10 days by expectation. Operation and repair times are mutually independent and exponentially distributed.

Provided that the machine is broken in the beginning of a month, what is the expected number of days it will be broken during the month (30 days)?

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