Customers arrive at a service station with the intensity A = 5 per hour. Assume that...

 

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Customers arrive at a service station with the intensity A = 5 per hour. Assume that customer arrivals form a Poisson process, X = (X(t): 20). Introduce for any natural k, such that k 21, the arrival times, W₁ = min [t≥ 01X(t) = k]. 1. Given that the eighth customer arrived exactly at the end of third hour, or Wa= 3, find the conditional density of the forth arrival time (W₁). 2. Evaluate E (W₁ Ws=3] and Var [W₁W=3] Customers arrive at a service station with the intensity A = 5 per hour. Assume that customer arrivals form a Poisson process, X = (X(t): 20). Introduce for any natural k, such that k 21, the arrival times, W₁ = min [t≥ 01X(t) = k]. 1. Given that the eighth customer arrived exactly at the end of third hour, or Wa= 3, find the conditional density of the forth arrival time (W₁). 2. Evaluate E (W₁ Ws=3] and Var [W₁W=3]

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To solve this problem well use the properties of Poisson processes Lets go through each part step by step Conditional Density of W4 given W8 3 Given t... View the full answer