I'm trying to do Question X5.8 & am confused by part (i). I'm doing the assignment without answers & want to be put in the right direction. My approach would be that I first need to calculate Beta, given I know the mean claim amount is £7,500. So if I have the pdf, then I need to calculate Beta such that 7,500 = integral (0 to infinity) of xf(x) dx. Using integration by parts, I get Beta = 2500. This makes no sense, as every time you put this large number in the exponential term, it will always be zero. This means that it is impossible to get a claim that hits the retention! Where am I going wrong?
It sounds like you are on the right lines, but I think your integration by parts has gone slightly wrong. Instead of integrating by parts, which can often get quite nasty, it's easier to re-write the integral of xf(x) dx as a constant term multiplied by the integral of a pdf. The integral term will therefore equal 1 and you'll be left with the constant term to equate with Beta. This is a commonly used "trick" to make the maths easier that you will have met in the earlier subjects. Good luck with the rest of the question...
