Mr. Jones is waiting to make a phone call from a public phone at a train...

Mr. Jones is waiting to make a phone call from a public phone at a train station. There are two public telephone booths next to each other, occupied by two persons, say A and B. If the duration of each phone call is an exponential random variable with λ = 1/6, what is the probability that among Mr. Jones, A, and B, Mr. Jones will not be the last to finish his call

Expert Solution

Answer:

To begin with, the likelihood that one of the two people on the telephone will complete before the other is 1 (the likelihood of both completing simultaneously is 0 on a persistent dissemination i.e., continuous distribution).

Presently that Mr. Jones can enter one of the stalls, he makes a call with exponentially distributed length.

Given the memory-less property of the exponential dissemination, Mr. Jones and the individual in the other corner presently have an equivalent possibility of completing before one another.

Hence, the likelihood that Mr. Jones won't be the last to complete his call is 0.5, which is irrational.

orchestra answered 2 years ago

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