Eatery Insurance is a company that focuses on insurances for cafes and restaurants. Eatery provides a risk parameter,to each policyholder. Based on the past data in Culver City, they observed that for a given =, claim sizes follow a Poisson distribution with parameter. On the other hand, their prior understanding for the distribution of has the following pdf

h()=1/^2,for1<<.

In 2021, we observed two claims, of sizes 1 and 2. Calculate the probability density function of the posterior distribution.