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Question: Automobiles arrive at a tollbooth on a highway completely at random according to a Poisson process with rate λ = 4 cars per hour. Determine the following:
a. The probability that the time between any two successive arrivals exceeds 20 minutes.
b. The probability that exactly four cars arrive in any given hour.
c. The probability that more than five cars arrive in any given hour.
d. The probability that more than 10 cars arrive in any given two-hour period.
e. A person working for the transportation department begins counting arrivals at the tollbooth at 8 A.M. What is the probability that he counts 20 arrivals before 12 noon? (Use a normal approximation for your calculations.)
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Now plot the error against 1: for the same range as in part (b) (you might want to use a log scale for the y-axis). How does the error behave? "What can you say about the accuracy of your algorithm? What can you say about the robustness of your alg..
Is the problem a convex optimization problem? If yes, give a complete proof. If no, explain why not, giving complete explanations
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