Statement of a problem № m41253


Consider the Poisson process of radioactive particle hits in Example 5.7.8. Suppose that the rate β of the Poisson process is unknown and has the gamma distribution with parameters α and γ. Let X be the number of particles that strike the target during t time units. Prove that the conditional distribution of β given X = x is a gamma distribution, and find the parameters of that gamma distribution.

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