Compute the probability that c leaves last

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Reference no: EM131266180

Three persons, A, B and C, get to a post office at the same time. They each want to make a telephone call. There are two telephone booths, which are immediately occupied by A and B. C makes her call after whoever finishes first. They leave the post office as soon as they have completed their calls. We denote by X, Y and Z the length of the telephone calls made by A, B and C, respectively. These three random variables are assumed to be i.i.d., their common law being exponential with parameter λ > 0.

1. Compute the probability that C leaves last.

2. Give the probability distribution of the total time T spent by C in the post office.

3. With 0 being the time of arrival of the three persons at the post office, give the probability distribution of the time of the last departure

Reference no: EM131266180

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