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At the airport, there are three counters for checking the luggage. The employees at each counter...

At the airport, there are three counters for checking the luggage. The employees at each counter work independently with the time for each customer modeled as an exponential distribution. The average time is one minute for one counter, two for the next, and three minutes for the third. An actuary, who is next in line, will take the next available counter, i.e. the minimum of the three.

What is the variance of the actuary's wait time?

Math   Statistics-And-Probability   
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