Question: You are tasked with operating a machine in a factory which malfunctions every X hours where X is a random variable with exponential distribution. You

You are tasked with operating a machine in a factory which malfunctions every X hours where X is a random variable with exponential distribution. You are told that on average the machine malfunctions every 8 hours. Your shift lasts 8 hours. If the machine malfunctions you are sent home early and paid $10 for your day of work. If the machine does not malfunction you earn $100 for your day of work. If the machine has been functioning for 8 hours when you arrive how much do you expect to earn for the day?

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