**Problem 5-A**

You are given the following:

- The number of claims in a calendar year for a given risk follows a Poisson distribution with mean .
- The prior distribution of has the following density function.

After observing for one calendar year, this risk is found to have incurred 4 claims.

Determine the Bayesian expected claim frequency for the given risk in the next year.

**Problem 5-B**

You are given the following:

- The number of claims in a calendar year for a given risk follows a Poisson distribution with mean .
- The prior distribution of has the following density function.

After observing for two calendar years, this risk is found to have incurred 2 claims in each year.

Determine the Bayesian expected claim frequency for the given risk in the next year.

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