3. Suppose you are the main actress in the movie: The Devil Wears Prada. In the

Question

3. Suppose you are the main actress in the movie: The Devil Wears Prada. In the movie, you are the second assistant of Miranda Priestly, the editor in chief of a fashion magazine called Runway, and your main task is to answer the phones. Since Miranda is so tough and she doesn’t want any phone calls to be missed, you have to stay at your desk. One day, however, you feel bursting and you really want to go to the restroom. Suppose X is the time between two calls, therefore, X follows an exponential distribution. And you know that:

(i). The average time between two phone calls is 10 minutes.

(ii). 3 minutes have passed since the last call.

(iii). You could leave your desk, go to the restroom, and come back in 1 minute.

By using what you have known so far, answer the following questions:

(a). Find the probability that no phone calls come within 1 minute from now (Note: from now means you are given the condition that 3 minutes have passed since the last call). (10pts)

(b). Will you leave the desk and go to the restroom at this time? Make your decision based on your answer in (b). (3pts)

Explanation / Answer

(a) as the given distribution is exponential distribution, this distribution has the memoryless proporty. That propoerty means that whatever will happen in future doesn't depend on what happened in past. So, if there are no phones from last 3 minute. That doesn't effect the probability of call comin in next 1 minute.

Here the = 1/10 = 0.1

So the probability that call will arrive in next 1 minute.

Pr(X < 1 minute) = 1 - e-0.1 = 0.0952

(b) No, i wouldn't leave and go to the restroom at this time as the probability is greater than 0.05. It will be 1 out of 10 probability that a call would come.

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