(a) Describe the applications of extreme value theory (EVT) in the following fields and give reference to key historical events.

(i) Insurance[2 marks]

(ii) Risk Management[2 marks]

(b) Determine the mean residual life for:

(i) the Exp() distribution[2 marks]

(ii) the Pa( ,) distribution where >1 .[2 marks]

(c) In a feasibility of a Wind Energy Farm with a consultant has suggested assessing the risk of damage by using the generalised Pareto distribution (GPD) to model the likelihood of wind speeds of above 150 miles per hour, using the country level wind data.

(i) Describe how this would be done. [4 marks]

(ii) What are the key challenges in modelling extreme events