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Math Help - Exponential Question

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    Exponential Question

    There are 4 customers in line at the bank teller's window. The length of time X in minutes needed to service a random customer has an exponential distribution with mean 5 minutes. As each customer finishes, the teller instantly starts the next customer. Assume the times needed to service the 4 customers are mutually independent.
    a) What is the mean and variance of the total amount of time needed to service the 4 customers?
    b) The bank will close in 15 minutes. What is the probability that the teller will finish servicing all 4 customers before the bank closes?
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    Quote Originally Posted by Janu42 View Post
    There are 4 customers in line at the bank teller's window. The length of time X in minutes needed to service a random customer has an exponential distribution with mean 5 minutes. As each customer finishes, the teller instantly starts the next customer. Assume the times needed to service the 4 customers are mutually independent.
    a) What is the mean and variance of the total amount of time needed to service the 4 customers?
    b) The bank will close in 15 minutes. What is the probability that the teller will finish servicing all 4 customers before the bank closes?
    Sum of exponentials is gamma. Figure out your parameters and your essentially done.
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