Question: A flashlight needs two batteries to be operational. You start with n batteries numbered 1 to n. Whenever a battery fails it is replaced by

A flashlight needs two batteries to be operational. You start with n batteries numbered 1 to n. Whenever a battery fails it is replaced by the lowest-numbered working battery. Suppose that battery life is exponential with mean 100 hours. Let T be the time at which there is one working battery left and N be the number of the one battery that is still good.

(a) Find ET.

(b) Find the distribution of N.

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