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Question X5.8

F

f888bet

Member
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...
 
Thanks Coralie,

I'd forgotten that method - it helped me spot my error.
 
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