Customer A and B are being served by two clerks in the post office. Customer C is waiting and he is the last customer of today. Suppose a clerk’s serving time for any customer follows exponential distribution with parameter λ independently. Customers will be served once any of the clerks are available. What’s the probability that customer A the last customer to leave the post office?
Customer A and B are being served by two clerks in the post office. Customer C is waiting and he is the last customer of today. Suppose a clerk’s serving time for any customer follows exponential distribution with parameter λ independently. Customers will be served once any of the clerks are available. What’s the
Let's consider the possible scenarios:
- Customer A is served first and leaves last.
- Customer B is served first and leaves last.
- Customer C is served first and leaves last.
To calculate the probability of each scenario, we can use the exponential distribution. The exponential distribution has a probability density function (PDF) of:
f(x; λ) = λ * e^(-λx)
Where:
- λ is the rate parameter.
- x is the time.
In this case, λ represents the rate at which the clerks serve customers, and we are given that the serving time follows an exponential distribution with parameter λ.
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