With Mr. Fantastic's help, I realized how to do my other set of problems. This time, I only have one problem. I will put the problem in quotes. Then my idea of how to do the problem after.
Should I first treat it as a deductible problem and find the mean of that. By this I mean:The total individual claim amount has a density function f(x)= (1/1000)e^-(x/1000); x(greater than or equal to)0. The premium is set at 100 over the expected claim amount. A portfolio consists of 100 independent policies with this claim distribution. Calculate the probability that the total claim amount exceeds total premiums collected.
The integral (min=0 max =100) of (1/1000)e^-(x/1000) + Integral (min=100 max = infinity) of (x-100)(1/1000)e^-(x/1000). This will give me the expected value of the premiums for each claim. I would multiply this by 100 to get the total expected premiums. I dont think I can treat this as a normal distribution because the problem does not say that it is normal.
Thanks in advance for the help.