**Part 1: Rainfall modelling [50 marks]**

The workspace rain.RData contains a dataframe with data on total amount of rainfall in milimeters at Exeter airport for the year 2019. There are three variables (columns): rain is the total hourly rainfall in mm, day_of_month is the associated day of the month, day_of_year is the associated day of the year, and hour is the hour of day. In this project, interest lies in understanding both the occurrence of hourly rainfall as well as the intensity (i.e. amount) when it does occur.

(a) Fit and present a statistical model that describe both rainfall occurrence and intensity.

(b) A company focusing on developing deterministic weather simulation models for the UK, wishes to test their model using data produced for Exeter airport in 2019. Column rainSim contains a specific simulation of hourly rainfall output from this model for 2019. Although the individual hourly values are not expected to be comparable, the distribution of hourly rainfall for that year should be the same if the deterministic weather is indeed able to simulate hourly rainfall well. Fit your model from (a) to rainSim, and use this to compare the rainfall distribution across the two data sets.

(c) Use your model from (a) to estimate the probability that the yearly total rainfall exceeds 9000mm.

Write a report on your investigation. Your report should include: a description and assumptions behind the statistical modelling; a statement of any parameter estimates and associated uncertainty, and an explanation of how you calculated them; model assessment (possibly referring to any other models that you considered); a statement of any estimated quantities and an explanation of how you calculated them; appropriate numerical and graphical evidence.

** Assessment criteria. **Of the 50 marks available for this part, approximately 32 are awarded for your choice, description assessment and discussion of your model(s), and 18 for compariring the distributions and for estimating the required probability