Question: 22. Suppose that a device is powered by a battery. Since an uninterrupted supply of power is needed, the device has a spare battery. When

22. Suppose that a device is powered by a battery. Since an uninterrupted supply of power is needed, the device has a spare battery. When the battery fails, the circuit is altered electronically to connect the spare battery and remove the failed battery from the circuit.

The spare battery then becomes the working battery and emits a signal to alert the user to replace the failed battery. When that battery is replaced, it becomes the new spare battery. Suppose that the lifetimes of the batteries used are independent uniform random variables over the interval (0, 1), where the unit of measurement is 1000 hours. For 0 < t ≤ 1, on average, how many batteries are changed by time t? How many are changed, on average, after 950 hours of operation?

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