A store is about to close for the day, and you are the only one working...

A store is about to close for the day, and you are the only one working there. The order is that you only close the store when all the clients are gone. There are still two (unrelated) clients in the store, and the time each stays in the store is modeled by an exponential random variable. We estimate that it would take in average 10 minutes for a client to exit the store.
(a) Model the time spent by the first client as a random variable T1 and the time spent by the second client T2. In words, what does T = max{T1, T2} represent? (b) Compute the CDF of T. (c) The two clients are still in the store and right at this moment a third client shows up. You decide to close the door, but the three clients that are still inside are welcome to take their time in the store. What is the chance that you still stay at least 20 more minutes?

Expert Solution

orchestra answered 2 years ago

A store is about to close for the day, and you are the only one working...

A store is about to close for the day, and you are the only one working there. The order is that you only close the store when all the clients are gone. There are still two (unrelated) clients in the store, and the time each stays in the store is modeled by an exponential random variable. We estimate that it would take in average 10 minutes for a client to exit the store. (a) Model the time spent by the...

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A store is about to close for the day, and you are the only one working...

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