The number of cracks in the tarmac per kilometer of road is assumed to follow a Poisson

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The number of cracks in the tarmac per kilometer of road is assumed to follow a Poisson process with rate \(\lambda\).

Your job is to find this rate for a lesser highway, and you have found 13 cracks in \(10 \mathrm{~km}\). Use neutral prior, and calculate the posterior probability distribution of \(\lambda\).

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