Question: An autonomous robot is slowly adapting to the environment, reducing the possibility of a fatal crash over time. It's hazard rate is given by (t)

An autonomous robot is slowly adapting to the environment, reducing the possibility of a fatal crash over time. It's hazard rate is given by (t) = 1t (for t > 0). Find the cumulative distribution function F and density f such that it has hazard rate (t) = 1t and use them to calculate the expected survival time of the robot.

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