Imber of customers arriving time = 1,2, ... Calculate the following condit time points 0< tj < t2< t3 < t4 : =1) = ?

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Customers arrive at a service station according to a Poisson process with a rate 2 = 3 per hour.
Denote by N+ the number of customers arriving until time t. Let Wn be the waiting time until the nth
customer arrives, n = 1,2, . Calculate the following conditional probabilities and conditional
expectations, for any time points 0 <t1<t2< t3 < t4:
i) PROB(Nt3=5| Nt1=1) = ?
ii) E(Nt2 | T2 > 1) = ?
Transcribed Image Text:Customers arrive at a service station according to a Poisson process with a rate 2 = 3 per hour. Denote by N+ the number of customers arriving until time t. Let Wn be the waiting time until the nth customer arrives, n = 1,2, . Calculate the following conditional probabilities and conditional expectations, for any time points 0 <t1<t2< t3 < t4: i) PROB(Nt3=5| Nt1=1) = ? ii) E(Nt2 | T2 > 1) = ?
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