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Recitation6sols

# Recitation6sols - Rensselaer Electrical Computer and...

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Rensselaer Electrical, Computer, and Systems Engineering Department ECSE 4500 Probability for Engineering Applications Recitation 6 Solution Wednesday March 3, 2010 Waiting time at a restaurant A certain restaurant has been found to have the following joint distribution for the waiting time for service for a newly arriving customer and the total number of customers including the new arrival. Let W be a random variable representing the continuous waiting time for a newly arriving customer, and let N be a discrete random variable representing the total number of customers. The joint distribution function is then given as, F W,N ( w, n ) = 0 , n < 0 or w < 0 , (1 exp w/μ 0 ) n 10 , 0 n 5 , w 0 , (1 exp w/μ 0 ) 5 10 + (1 exp w/μ 1 ) ¡ n 5 10 ¢ , 5 < n < 10 , w 0 , (1 exp w/μ 0 ) 5 10 + (1 exp w/μ 1 ) ¡ 5 10 ¢ , 10 n, w 0 , where the parameters μ i satisfy 0 < μ 0 < μ 1 . Note that this choice of the parameters means that waiting times are longer when the number of customers is large.

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Recitation6sols - Rensselaer Electrical Computer and...

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