Cars pass a certain street location according to a Poisson process with rate A=1 per minute. A woman who wants to cross the street at that location waits until she can see that no cars will come by in the nextT =2 minutes. Find her expected waiting time. Round answer to 2 decimals. Hints: • Figure out what is p = the probability of an interarrival time >T Show that waiting for an interarrival >T is a geometric random variable with success probability p Recall Wald's equation. • You will need to think about what is the expected value of an interarrival time that takes less than 2 minutes. E(T |T<2)
Cars pass a certain street location according to a Poisson process with rate A=1 per minute. A woman who wants to cross the street at that location waits until she can see that no cars will come by in the nextT =2 minutes. Find her expected waiting time. Round answer to 2 decimals. Hints: • Figure out what is p = the probability of an interarrival time >T Show that waiting for an interarrival >T is a geometric random variable with success probability p Recall Wald's equation. • You will need to think about what is the expected value of an interarrival time that takes less than 2 minutes. E(T |T<2)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Cars pass a certain street location according to a Poisson process with rate A=1 per minute.
A woman who wants to cross the street at that location waits until she can see that no cars will come by in the next T =2 minutes. Find her expected waiting time. Round answer to 2
decimals.
Hints:
Figure out what is p = the probability of an interarrival time > T
Show that waiting for an interarrival >T is a geometric random variable with success probability p
• Recall Wald's equation.
• You will need to think about what is the expected value of an interarrival time that takes less than 2 minutes. E(T | T<2)
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