Poisson Process and Stress Fractures in Railway Lines

AI Thread Summary
The discussion revolves around a homework problem involving a Poisson process where stress fractures in railway lines occur at a rate of 2 per month. For part (a), the probability of the 4th stress fracture occurring 3 months after checking the lines is calculated using the Poisson probability formula, though there is confusion regarding the constants used. In part (b), the expected time for the 4th stress fracture to occur is also derived using a similar probability function, prompting questions about the calculations and confidence levels. Participants seek clarification on the correct formulas and constants for both parts of the problem. The conversation highlights the complexities involved in applying Poisson processes to real-world scenarios like railway maintenance.
Jenny123
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Homework Statement


Suppose that stress fractures appear in railway lines according to a Poisson process at a rate of 2 per month.
a)Find the probability that the 4th stress fracture on the railway line occurred 3 months after the process of checking the new railway lines.

b)Suppose new railway lines have just been laid, how long (in months) is it expected to take for the 4th stress factor to occur?


Homework Equations





The Attempt at a Solution


a) P(N(3) =3) = (54 exp{-6} )/3!

b) P(N(4) =4) = (512 exp{-8})/4!
 
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What is your formula for the probability function? I don't see how you get 54 in part a.
You appear to use the same probability estimation to determine the number of months in b. Is there a confidence level for b?
 
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