# Math Help - Density Function

1. ## Density Function

The total claim amount for a health insurance policy follows a distribution with density function f(x)= e^(-x/1000)/1000 for x>0. The premium for the policy is set at 100 over the expected total claim amount. If 100 policies are sold, what is the approximate probability that the insurance company will have claims exceeding the premiums collected?

2. Originally Posted by affelix
The total claim amount for a health insurance policy follows a distribution with density function f(x)= e^(-x/1000)/1000 for x>0. The premium for the policy is set at 100 over the expected total claim amount. If 100 policies are sold, what is the approximate probability that the insurance company will have claims exceeding the premiums collected?
E(X) = 1000 (why?).

Calculate $p = \Pr(X > 1100)$ using the given pdf.

Let Y be the random variable number of premiums exceeding \$1100.

Y ~ Binomial(n = 100, p = value calculated above).

Calculate Pr(Y > 0) = 1 - Pr(Y = 0).