1 (a) Download the Oxford meteorological station historic data1 . Keep the monthly sun hours data for the period 1929-2022. Extract the 12 month block maxima data, plot it and its empirical cumulative distribution function. 3 marks (b) Fit a Generalized Extreme Value (GEV) distribution to the block maxima data from part (a). Report the MLE estimates of the GEV parameters, analyse their meaning and draw conclusions about the limiting distribution of the maxima. 4 marks (c) Briefly explain how P-P and Q-Q plots are constructed, generate them and use them to comment on the quality of the fit from part (b). 3 marks (d) Perform a goodness of fit test of the fit from part (b), using Kolmogorov Smirnov and Cramer von Mises tests and comment on the results providing the corresponding statistical inference. 3 marks (e) Briefly explain what is the meaning of a return level and return period. Calculate the 5 year return level of a maximum sunlight event. What is the return period of 280 hours of sunlight in one month. Explain your results using appropriate wording. 4 marks Total: 17 marks