**Problem 1-A**

You are given:

- The claim size for a policyholder randomly chosen from a large group of insureds is a mixture of a Burr distribution with , and and a Pareto distribution with and .
- The mixture distribution of has equal mixing weights.

Calculate the median of .

**Problem 1-B**

You are given:

- The claim size in the current year for a policyholder randomly chosen from a large group of insureds is a mixture of a Burr distribution with , and and a Pareto distribution with and .
- The mixture distribution of has mixing weights 90% (for the Burr distribution) and 10% (for the Pareto distribution).
- Suppose that the claim size for the chosen policyholder in the next year will increase 20% due to inflation.

What is the probability that the claim size in the next year will exceed 50?

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