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Dropouts on a data feed

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Dropouts on a data feed follow a Poisson process with rate $λ$ per week. The prior on $λ$ is a Gamma distribution with shape $4$ and rate $2$ . Over $6$ weeks you count $14$ dropouts in total. What is the posterior mean of $λ$ ? Give a fraction.

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Hint

Add events to the shape and weeks to the rate.

Solution

The posterior shape is $4 + 14 = 18$ and the posterior rate is $2 + 6 = 8$ .
The posterior mean is $\frac{18}{8} = \frac{9}{4}$ .

Answer: $\frac{9}{4}$

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