If you have observed data from a Poisson distribution with arrival rate x over t time...

If you have observed data from a Poisson distribution with arrival rate x over t time units (e.g., k events in t time units), and your prior distribution for x was gamma distributed, show that the posterior distribution for the arrival rate x is also gamma distributed. (Hint: You will need to evaluate a definite integral in the denominator of the expression for the posterior distribution

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