A coastal region is susceptible to frequent thunder storms which last for several hours. The total number of houses that suffer some type of damage, during such a storm, follow a Poisson process with rate = 3 per hour. The insurance approves any claim if the cost of repairing the damage is over $2000. The total cost of repair for every house follows a Normal distribution with a mean of $3000 and standard deviation of $750. Also the cost of repair is independent of the total number of damages. (a) What is the mean and the standard deviation of the total cost of repair during a storm that lasted for 5 hours? (b) What is the probability that the insurance company will have to approve at least 3 claims filed for damages of houses after a storm that lasted for 5 hours? (c) Describe how a Non-homogeneous Poisson process could be appropriate in this situation. Write the associated stochastic process for your proposed model along with your own proposed intensity function. Justify your choices clearly. You should write in a way as if you are describing it to someone not having much knowledge on the topic.