The number of traffic accidents at a certain intersection is thought to be well modeled by a Poisson process with a mean of 3.5 accidents per year.

Find the mean waiting time between accidents and find the standard deviation of the waiting times between accidents.

I assumed $\mu$ = $\lambda$ and $\sigma$$^2$ = $\lambda$, but that didn't seem to work. I've been looking at multiple formulas, including the Poisson ones, and I can't figure out how to even begin to figure this out. I could use a step in the right direction


3.5 accidents per year implies one accident per 1/3.5 years = 0.28 years. This is the mean waiting time between accidents.

The variance of the waiting time will also be 0.28 years, meaning that the standard deviation is its square root, 0.535 years.

EDIT: I made an error. lambda = 3.5, so mean interarrival time is 1/lambda = 0.28 years; however, the variance of the interarrival time is 1/(lambda^2), meaning the standard deviation of the interarrival time is 0.28 years

Read more here: https://www.kellogg.northwestern.edu/faculty/weber/decs-430/Notes%20on%20the%20Poisson%20and%20exponential%20distributions.pdf


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